Module 6 · Modern Mathematics
Chapter 56: Mathematical Reasoning
Modern Mathematics
3 topics
What this chapter covers
The 3 topics below make up Mathematical Reasoning on the CAT. Click any topic to open its notes, examples and practice test.
Study material & tests
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Formula Reference Sheet
This chapter
Connectives & negation
| Negation | ¬p is true exactly when p is false |
|---|---|
| Conjunction (AND) | p ∧ q true only when both p and q are true |
| Disjunction (OR) | p ∨ q false only when both p and q are false |
| Implication | p → q false only when p is true and q is false |
| Biconditional | p ↔ q true when p and q have the same truth value |
Logical identities (CAT power-tools)
| Contrapositive (equivalent) | (p → q) ≡ (¬q → ¬p) |
|---|---|
| Implication as OR | (p → q) ≡ (¬p ∨ q) |
| De Morgan (AND) | ¬(p ∧ q) ≡ ¬p ∨ ¬q |
| De Morgan (OR) | ¬(p ∨ q) ≡ ¬p ∧ ¬q |
| Negation of quantifiers | ¬(∀x P) ≡ ∃x ¬P; ¬(∃x P) ≡ ∀x ¬P |
CAT reference
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