Tier 1: Propositional Logic
Conditionals and Deductive Reasoning
Analyze conditional statements, write logical variations, and identify valid laws of deduction.
1. Which law justifies: 'If p -> q is true, and p is true, then q is true'?
A) Law of SyllogismB) Law of DetachmentC) Law of ContrapositionD) Transitive Property
2. Which variation of a conditional statement is always logically equivalent to the original conditional statement?
A) ContrapositiveB) ConverseC) InverseD) Biconditional
3. The statement formed by negating both the hypothesis and conclusion of p -> q is the ____.
4. A conditional statement and its converse always share the exact same truth value.
TrueFalse
5. Write the contrapositive of: 'If two lines are perpendicular, then they intersect at right angles.'
6. Match each symbolic logical form to its correct technical title:
| p -> q | • | • | Converse |
| q -> p | • | • | Inverse |
| ~p -> ~q | • | • | Contrapositive |
| ~q -> ~p | • | • | Conditional |
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