Question

a) select the inverse of:
if you dont eat your meat, then you cant have any pudding.

• if you eat your meat, then you cant have any pudding.
• eat your meat or you cant have any pudding.
• if you dont eat your meat, then you can have some pudding.
• if you are having pudding, then you ate your meat.
• if you eat your meat, then you can have some pudding.
• if you cant have any pudding, then you didnt eat your meat.

b) select the contrapositive of:
if you dont eat your meat, then you cant have any pudding.

• if you eat your meat, then you can have some pudding.

Explanation:

Identify the components of the conditional statement

Let \(p\) be "you don't eat your meat" and \(q\) be "you can't have any pudding".
The original statement is \(p
ightarrow q\).

Determine the inverse statement

The inverse of \(p
ightarrow q\) is \(
eg p
ightarrow
eg q\).
\(
eg p\): "you eat your meat"
\(
eg q\): "you can have some pudding"
Inverse: "If you eat your meat, then you can have some pudding."

Determine the contrapositive statement

The contrapositive of \(p
ightarrow q\) is \(
eg q
ightarrow
eg p\).
\(
eg q\): "you can have some pudding"
\(
eg p\): "you eat your meat"
Contrapositive: "If you can have some pudding, then you ate your meat." (or "If you can have some pudding, then you eat your meat.")
Looking at the visible option for part b: "If you eat your meat, then you can have some pudding" is the inverse, not the contrapositive. However, we must select the correct option representing the contrapositive \(
eg q
ightarrow
eg p\).

Answer:

Question 1

• If you eat your meat, then you can't have any pudding.
• Eat your meat or you can't have any pudding.
• If you don't eat your meat, then you can have some pudding.
• If you are having pudding, then you ate your meat.
• If you eat your meat, then you can have some pudding. (Correct answer)
• If you can't have any pudding, then you didn't eat your meat.

Question 2

• If you can have some pudding, then you ate your meat. (Correct answer)
• If you eat your meat, then you can have some pudding.