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Write the converse, inverse, and contrapositive of the given conditional statement below

Write the converse, inverse, and contrapositive of the given conditional statement-example-1

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Answer:

Converse: B. If x = 5, then 4x + 7 = 27

Inverse: If 4x + 7 ≠ 27, then x ≠ 5

Contrapositive: If x ≠ 5, then 4x + 7 ≠ 27

Explanations:

To find the converse of a statement, the hypothesis should become the conclusion, and vice-versa.

That is, for a statement like:

If P, then Q, P → Q

The converse will be:

If Q, then P, Q→ P

Following the rule above, the converse of the statement:

"If 4x + 7 = 27, then x = 5" will be

" If x = 5, then 4x + 7 = 27"

For a statement "

If P, then Q, P → Q

The inverse will be:

If ∼P, then ∼Q, ∼P → ∼Q

Following the rule above, the inverse of the statement:

"If 4x + 7 = 27, then x = 5" will be

"If 4x + 7 ≠ 27, then x ≠ 5 "

For a statement, " If P, then Q", the contrapositive will be "If not Q, then not P"

If P, then Q, P → Q

The contrapositive will be:

If ∼Q, then ∼P, ∼Q → ∼P

Following the rule above, the converse of the statement:

"If 4x + 7 = 27, then x = 5" will be

" If x ≠ 5, then 4x + 7 ≠ 27"

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