Question

Consider the following conditional statement: If today is Monday, then tomorrow is Tuesday Here are some variants of that statement:A.If today is not Monday, then tomorrow is not Tuesday.B.If tomorrow is Tuesday, then today is Monday.C.If tomorrow is not Tuesday, then today is not Monday.(a) Which statement is the inverse? (A/B/C)(b) Which statement is the converse? (A/B/C)(c) Which statement is the contrapositive? (A/B/C)

Answer 1

Question A:

The answer is Inverse

Question B:

The answer is Converse

Question C:

The answer is Contrapositive

SOLUTION

Problem Statement

The question gives us a statement and we are asked to find its inverse, converse, and contrapositive. The statement given is:

`\text{ }^(\prime)\text{ If today is Monday, then tomorrow is Tuesday'}`

Method

To solve this question, we need to know the definitions for each of inverse, converse, contrapositive.

Given the original statement, "If p, then q"

Inverse:

`\text{' If not p, then not q'}`

Converse

`^(\prime)\text{ If q then p'}`

Contrapositive:

`\text{' If not q then not p'}`

With these definitions, we can solve the question.

Implementation

Let p be "today is Monday".

Let q be "tomorrow is Tuesday"

Thus, the original statement can be written as:

`^(\prime)\text{ If p then q'}`

Question A:

If today is not Monday, then tomorrow is not Tuesday.

If p is "today is Monday" and q is "tomorrow is Tuesday"

Then, we can re-write the statement as follows:

"if not p then not q"

This corresponds to Inverse

Question B:

"If tomorrow is Tuesday, then today is Monday."

This can be re-written as:

"If q, then p"

This corresponds to Converse

Question C:

"If tomorrow is not Tuesday, then today is not Monday"

This can be re-written as:

"if not q, then not p"

This corresponds to Contrapositive

Final Answer

Question A:

The answer is Inverse

Question B:

The answer is Converse

Question C:

The answer is Contrapositive