Question

a conditional statement is given below. give the converse, contrapositive, and inverse of the statement. also use the table above to decide if it is true or false. assume that any light - bulb mentioned was sold at the store. given statement: if a light - bulb cost $4, then the light - bulb was red. converse: if a light - bulb cost $4, then the light - bulb was not red. contrapositive: if a light - bulb was not red, then the light - bulb did not cost $4. inverse: if a light - bulb was red, then the light - bulb did not cost $4.

Explanation:

Step1: Define conditional statement

Let the original conditional statement be \(p
ightarrow q\), where \(p\) is "a light - bulb cost \(\$4\)" and \(q\) is "the light - bulb was red".

Step2: Find the converse

The converse of \(p
ightarrow q\) is \(q
ightarrow p\), i.e., "If the light - bulb was red, then the light - bulb cost \(\$4\)". Just because a light - bulb is red doesn't mean it costs \(\$4\), so it is false.

Step3: Find the contrapositive

The contrapositive of \(p
ightarrow q\) is \(
eg q
ightarrow
eg p\), i.e., "If the light - bulb was not red, then the light - bulb did not cost \(\$4\)". There could be non - red light - bulbs that cost \(\$4\), so it is false.

Step4: Find the inverse

The inverse of \(p
ightarrow q\) is \(
eg p
ightarrow
eg q\), i.e., "If a light - bulb did not cost \(\$4\), then the light - bulb was not red". There could be non - \(\$4\) red light - bulbs, so it is false.

Answer:

Converse: False
Contrapositive: False
Inverse: False