Analytical Ability • Topic 2 of 4 Professional Only 100% Free CSE Learning Resources

Symbolic Logic, Syllogisms & Abstract Reasoning

Conditional rules (If P, then Q), Venn Diagram method para sa All/Some/No, at visual pattern rules sa Abstract Reasoning.

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Category: Analytical Ability • Topic 2 of 4
Exam Area: Analytical Ability
Professional Only • Topic 2 of 4

Symbolic Logic, Syllogisms & Abstract Reasoning

Sa paksang ito, gagawin nating simple at biswal ang tatlong paboritong logic topics sa CSE Professional Exam: Conditional Rules (If P, then Q), Syllogisms (All, Some, No), at Abstract Reasoning (hugis, simbolo, at galaw).

Learning Objectives:
  • Malaman kung aling konklusyon ang 100% valid sa Conditional Logic (If P, then Q): Direct (Modus Ponens) at Contrapositive (~Q → ~P).
  • Magamit ang Venn Diagram Method (pag-drawing ng bilog) para sa All, No, at Some syllogism statements.
  • Ma-solve nang mabilis ang Abstract Reasoning sequences sa pamamagitan ng paghihiwalay ng Rotation, Position Shift, Counting, at Shading rules.
  • Maiwasan ang Converse at Inverse logic fallacies na madalas ipain sa choices.
Bakit mahalaga sa CSE: Sa Logic at Syllogisms, itabi muna ang personal na opinyon—tanggapin na 100% totoo ang Premises kahit kakaiba pakinggan, at piliin lang ang Conclusion na siguradong-sigurado (guaranteed) sa bawat pagkakataon.
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Subtopic 1 • Conditional & Symbolic Logic

Conditional Rules: "If P, then Q" (P → Q)

Alin lang ang dalawang konklusyon na 100% sigurado kapag may 'If... then...' rule?

Kapag binigyan ka ng conditional statement na If P, then Q (halimbawa: "If an employee passes the CSE Professional exam (P), then they earn First-Grade eligibility (Q)"), dalawa lang ang valid deduction at dalawa ang laging bitag (invalid fallacy):

Concept Diagram Syllogism Venn Diagrams & Conditional Logic Rules (P → Q)
Diagram na nagpapakita ng Venn Diagram para sa All A are B at No B are C sa kaliwa, at Conditional Logic rules (Modus Ponens, Contrapositive, at Invalid Converse/Inverse traps) sa kanan
Sa P → Q, tanging ang P → Q (Direct) at ~Q → ~P (Contrapositive) lamang ang 100% tiyak!
Visual Takeaway: Kapag binaligtad mo ang P → Q, kailangan mo ring lagyan ng NOT ang parehong dulo (~Q → ~P). Kung binaligtad mo lang nang walang NOT (Q → P), mali iyon!
Core Rule • Conditional Logic

Ang 2 Valid Rules vs. 2 Invalid Traps sa Symbolic Logic (P → Q)

  • ✓ VALID #1 — Direct Rule (Modus Ponens: P → Q): Nangyari ang P, kaya siguradong mangyayari ang Q.
  • ✓ VALID #2 — Contrapositive Rule (Modus Tollens: Not Q → Not P): Hindi nangyari ang Q, kaya siguradong hindi rin nangyari ang P!
  • ✗ TRAP #1 — Converse Error (Q → P is UNCERTAIN/INVALID): Nangyari ang Q, ibig bang sabihin ay P agad ang dahilan? Hindi sigurado! (Hal. Kung basa ang kalsada, hindi ibig sabihin ay umulan—baka nagdilig lang!).
  • ✗ TRAP #2 — Inverse Error (Not P → Not Q is UNCERTAIN/INVALID): Hindi nangyari ang P, ibig bang sabihin ay hindi na mangyayari ang Q? Hindi rin sigurado!
Key Takeaway: Tandaan: P → Q ay laging katumbas ng NOT Q → NOT P (Contrapositive)!
Halimbawa / Direct Example

Sample CSE Conditional Logic Question (Contrapositive)

Given the rule: 'If an infrastructure project exceeds ₱50 million (P), it must undergo a comprehensive audit by the special committee (Q).'

Fact: Project Tulay did NOT undergo a comprehensive audit by the special committee (~Q).

Which conclusion must be true?
A Project Tulay was canceled by the agency.
B Project Tulay did not exceed ₱50 million.
C Project Tulay exceeded ₱50 million but was exempted.
D All projects under ₱50 million are never audited.
Tamang Sagot: Choice B (Project Tulay did not exceed ₱50 million.)
Paliwanag: Ito ay eksaktong Contrapositive (~Q → ~P): Kung lahat ng lagpas ₱50M ay kailangang dumaan sa special audit (P → Q), at ang Project Tulay ay HINDI dumaan sa special audit (~Q), siguradong HINDI ito lumagpas sa ₱50 million (~P).
'Choice D — MALI (Inverse Fallacy: ~P → ~Q)', 'detail' => 'Hindi sinabi ng rule na bawal i-audit ang nasa baba ng ₱50M; sinabi lang kung ano ang mangyayari kapag lumagpas sa ₱50M.', ], [ 'title' => 'Choice B — TAMA (100% Guaranteed by ~Q → ~P)', 'detail' => 'Dahil ~Q (no special audit), siguradong ~P (did not exceed ₱50 million).', ], ]" finalAnswer="Choice B" />
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Subtopic 2 • Categorical Syllogisms

Syllogisms: Ang Venn Diagram Method (All, No, Some)

Huwag malito sa salita—mag-drawing ng simpleng bilog sa scratch paper!

Sa Syllogisms, bibigyan ka ng dalawa o tatlong statements na may All, No, o Some. Narito kung paano sila i-drawing:

Core Rule • Venn Diagrams

3 Bilog Rules sa Syllogisms

  • 1. All A are B (Maliit na bilog sa loob ng malaking bilog): Iguhit ang bilog A nang buong-buo sa loob ng bilog B. (Sigurado: Some B are A; Hindi sigurado: All B are A).
  • 2. No A are B (Dalawang magkahiwalay na bilog): Iguhit ang bilog A at bilog B na walang overlap. (Sigurado: No B are A).
  • 3. Some A are B (May × sa intersection): Mag-overlap ng bahagya ang A at B. Tandaan: kapag parehong "Some" lang ang premises (hal. Some A are B at Some B are C), WALANG siguradong koneksyon sa pagitan ng A at C!
Key Takeaway: Ang 'All A are B' ay HINDI nangangahulugang 'All B are A'! Ang maliit na bilog na A ay nasa loob ng malaking bilog na B.
Halimbawa / Direct Example

Sample CSE Syllogism Question

Statements:
1. All certified auditors are detail-oriented professionals.
2. No detail-oriented professional is careless with records.

Which of the following conclusions is 100% logically valid?
A All detail-oriented professionals are certified auditors.
B No certified auditor is careless with records.
C Some certified auditors are careless with records.
D Anyone who is not careless with records is a certified auditor.
Tamang Sagot: Choice B (No certified auditor is careless with records.)
Paliwanag: Ang bilog ng 'Certified Auditors' (A) ay nasa loob ng 'Detail-Oriented Professionals' (B). Dahil ang buong bilog (B) ay hiwalay na hiwalay sa 'Careless with Records' (C), siguradong walang kahit isang Certified Auditor (A) ang nasa loob ng (C)!
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Subtopic 3 • Abstract & Symbol Reasoning

Abstract Reasoning: Paano Basahin ang Pattern ng Hugis at Simbolo

Ihiwalay ang bawat elemento (isa-isang tingnan ang ikot, puwesto, bilang, at kulay).

Kapag nakakita ng Abstract Reasoning o Symbol Sequence, nakakalula ito kung titingnan mo ang buong kahon nang sabay-sabay. Ang sikreto: pumili muna ng ISANG elemento lang (halimbawa, ang gitnang arrow lang) at sundan ang galaw nito mula Frame 1 hanggang Frame 4!

Concept Diagram Abstract Reasoning Sequence: Tracking Rotation, Position & Shading
5-frame visual sequence na nagpapakita ng Arrow 90-degree clockwise rotation, Corner Circle 1-step clockwise movement, at Dark/Hollow shading alternation
Bawat frame ay sumusunod sa 3 simpleng rules nang sabay: (1) Ikot ng arrow, (2) Lipat ng kanto ng bilog, at (3) Palit ng kulay.
Visual Takeaway: Sa Frame 1→2→3→4, ang arrow ay ↑ → ↓ ← kaya sa Frame 5 ay ↑ ulit. Ang bilog ay TL → TR → BR → BL kaya sa Frame 5 ay TL ulit. Ang kulay ay ● → ○ → ● → ○ kaya sa Frame 5 ay ● (Dark) ulit!
Core Rule • Abstract Patterns

Ang 4 Standard Rules sa Abstract & Symbol Sequences

  1. 1. Rotation (Ikot): Umiikot ba ang hugis nang Clockwise (CW) o Counterclockwise (CCW) nang 45° (kalahating kanto), 90° (isang kanto), o 180° (baligtad)?
  2. 2. Position Shift (Galaw sa Kanto/Linya): Lumilipat ba ang maliit na simbolo nang 1 step clockwise sa paligid ng kahon (Top-Left → Top-Right → Bottom-Right → Bottom-Left)?
  3. 3. Progression / Counting (Bilang ng Guhit o Gilid): Nadadagdagan ba ng +1 ang bilang ng gilid o tuldok (hal. Triangle (3) → Square (4) → Pentagon (5) → Hexagon (6))?
  4. 4. Shading / Polarity Alternation (Kulay): Nagpapalit-palit ba ang kulay (Black ● → White ○ → Black ● → White ○)?
Key Takeaway: I-check ang isang rule at mag-eliminate agad ng choices bago pa tingnan ang pangalawang rule!
Halimbawa / Direct Example

Sample Symbol & Alphanumeric Logic Sequence

Look at the symbol-code sequence below. Each item consists of an arrow, a polygon-side number, and a corner letter:

[ ↑ • 3A ] → [ → • 4B ] → [ ↓ • 5C ] → [ ← • 6D ] → _____

Which item comes next in the sequence?
A [ ↓ • 7E ]
B [ ↑ • 7E ]
C [ ↑ • 6E ]
D [ → • 7D ]
Tamang Sagot: Choice B ([ ↑ • 7E ])
Paliwanag: Rule 1 (Arrow): Umiikot nang 90° clockwise (↑, →, ↓, ←, kaya susunod ay ↑). Rule 2 (Number): Tumataas ng +1 (3, 4, 5, 6, kaya susunod ay 7). Rule 3 (Letter): Sunod-sunod sa alpabeto (A, B, C, D, kaya susunod ay E).
One-Element Elimination Hack sa Abstract Reasoning
Sa halimbawa sa itaas, tingnan lang muna ang Arrow: ↑, →, ↓, ← → ang susunod ay ↑. Sa isang tingin lang, tanggal na agad ang Choice A (↓) at Choice D (→)! Tapos tingnan ang numero (3, 4, 5, 6 → 7), tanggal na rin ang Choice C (6). Nakuha mo ang Choice B nang walang kahirap-hirap!

Short Recap: Symbolic Logic, Syllogisms & Abstract Reasoning

  • Sa Conditional Logic (If P, then Q), tanging ang Direct Rule (P → Q) at Contrapositive (Not Q → Not P) lamang ang 100% valid.
  • Huwag malinlang sa Converse (Q → P) at Inverse (Not P → Not Q)—parehong hindi sigurado ang mga ito.
  • Sa Syllogisms, i-drawing ang bilog: All A are B (A sa loob ng B), No A are B (magkahiwalay), at Some A are B (may overlap).
  • Sa Abstract Reasoning, huwag tingnan ang buong larawan nang sabay—sundan nang paisa-isa ang Rotation, Position, Count, at Shading.
Supplementary Video References

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