Question

For each of the following statements, write negation, contrapositive, converse and inverse. . If P is a square, then P is a rectangle .If n is prime, then n is odd or n is 2 .If 2 is a factor of n and 3 is a factor of n, then 6 is a factor of n

Answer 1

Step-by-step explanation:

Consider the provided information.

For the condition statement $p \rightarrow q$ or equivalent "If p then q"

• The rule for Converse is: Interchange the two statements. $q \rightarrow p$
• The rule for Inverse is: Negative both statements. $\sim p \rightarrow \sim q$
• The rule for Contrapositive is: Negative both statements and interchange them. $\sim q \rightarrow \sim p$

• The rule for Negation is: If p then q" the negation will be: p and not q. $p \rightarrow q=\sim p\vee q=p\vee \sim q$

Part (A) If P is a square, then P is a rectangle.

Here p is "P is a square", and q is "Hill and P is a rectangle".

Negation: P is a square and P is not a rectangle.

Contrapositive: If P is not a rectangle then p is not a square.

Converse: If P is a rectangle then P is a square.

Inverse: If P is not a square then P is not a rectangle.

Part (B) If n is prime, then n is odd or n is 2

Here p is "n is prime", and q is "n is odd or n is 2".

Negation: n is prime and n is even and n is not 2.

Contrapositive: If n is not odd or n is not 2 then n is not prime.

Converse: If n is odd or n is 2 then n is prime.

Inverse: If n is not prime, then n is not odd or n is not 2.

Part (C) If 2 is a factor of n and 3 is a factor of n, then 6 is a factor of n.

Here p is "2 is a factor of n and 3 is a factor of n", and q is "6 is a factor of n".

Negation: 2 is a factor of n and 3 is a factor of n and 6 is not a factor of n.

Contrapositive: If 6 is not a factor of n then 2 is not a factor of n and 3 is not a factor of n.

Converse: If 6 is a factor of n then 2 is a factor of n and 3 is a factor of n.

Inverse: If 2 is not a factor of n and 3 is not a factor of n, then 6 is not a factor of n