Let's consider each of the statements one at a time using the given p and q.
p: & 3x-7=20
q: & x=9
Conditional Statement
We can write the conditional statement, p→ q, in an if-then form.
If 3x-7=20,
then x=9.To determine if this is true, we substitute the value of x into the equation and check if the left-hand side and right-hand side are equal.
The solution is correct. Therefore, we can claim that the conditional statement is true.
Converse
The converse of a conditional statement, q→ p, exchanges the hypothesis and the conclusion of the conditional statement.
If x=9 ,
then 3x-7=20 .
By the same logic the conditional statement is true, the converse of the conditional statement is also true.
Inverse
The inverse of a conditional statement, ~ p→ ~ q, requires us to negate the hypothesis and the conclusion of the conditional statement.
If 3x-7≠20,
then x≠9.
This is a true statement. If 3x-7 does not equal 20 the value of x cannot be 9, as this would make 3x-7 equal 20.
Contrapositive
The contrapositive of a conditional statement, ~ q→ ~ p, starts out with the converse of the conditional statement. Then we have to negate the hypothesis and the conclusion.
If x≠9 ,
then 3x-7≠20 .
By the same logic we know that the previous statements are true, we know that the contrapositive is true.
