Question

Determine the statement that is logically equivalent to this conditional statement.

If you have a small lawn to mow, then you do not live in a mansion.
A)
If you have a small lawn to mow, then you live in a mansion.
B)
If you do not have a small lawn to mow, then you live in a mansion.
If you live in a mansion, then you do not have a small lawn to mow.
D)
If you do not live in a mansion, then you have a small yard to mow.

Answer 1

C) If you live in a mansion, then you do not have a small lawn to mow.

Explanation:

Statement is

• If you have a small lawn to mow, then you do not live in a mansion.
• "If p then q"

Equivalent statement as per the rule should be:

• 1. Not p or q
• 2. q or not p
• 3. If not q then not p

Options to identify equivalent statement

A) If you have a small lawn to mow, then you live in a mansion.

• False

B) If you do not have a small lawn to mow, then you live in a mansion.

• False

C) If you live in a mansion, then you do not have a small lawn to mow.

• True as per rule 3 above

D) If you do not live in a mansion, then you have a small yard to mow.

• False

Correct answer is option C)