RTUComputer ScienceYr 2024 · Sem 42024

Q3Discrete Mathematics Structure

Question

4 marks

State the converse, inverse and contrapositive of the statement "If today is Easter, then tomorrow is Monday". Also construct truth table.

Answer

Let p: today is Easter, q: tomorrow is Monday. p → q is given.

Converse ( $q \to p$ ): If tomorrow is Monday, then today is Easter.
Inverse ( $\sim p \to\sim q$ ): If today is not Easter, then tomorrow is not Monday.
Contrapositive ( $\sim q \to\sim p$ ): If tomorrow is not Monday, then today is not Easter.

Truth Table:

Constructing the table for $p \to q$ and its variations confirms they are not all equivalent, except for the conditional and its contrapositive.