Question

a) Describe at least five different ways to write the conditional statement\(p \to q\)in English.

b) Define the converse and contrapositive of a conditional statement.

c) State the converse and the contrapositive of the conditional statement “If it is sunny tomorrow, then I will go for a walk in the woods.”

Short answer

Five different ways are as- “if p, then q”;“p, implies q”;“if p, q”;“p is sufficient for q”;“q when p”.

The converse of the conditional statement is “If Q then P”. The contrapositive of the conditional statement is “If not Q then not P”.

Step-by-step solution

Introduction

The conditional statement of p and qcan be denoted by P→q, which can be read as “if p, then q”. The conditional statement P→qis false when p is true and q is false, and is true in all other cases.

Ways for depiction of conditional statement

(a) Different ways to write the conditional statementP→qin English.

“if p, then q”

“p, implies q”

“if p, q”

“p is sufficient for q”

“q when p”

“q follows from p

“a necessary condition for p is q”

“q whenever p”

Converse conditional

(b) The converse of conditional statementP→q is\(q \to p\)

The contrapositive of a conditional statementP→qis\( - q \to - p\).

Converse and Contrapositive of statement

(c) The converse of “If it is sunny tomorrow then I will go for a walk in the woods” is “If I will go for a walk in the woods then it is sunny tomorrow.”

The contra-positive of “If it is sunny tomorrow then I will go for a walk in the woods” is “If I will not go for a walk in the woods then it is not sunny tomorrow.”