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Given the conditional statement, write the converse inverse, contrapositive, and Bi-conditional."2+2=4,ℎ=1."

User Ishio
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Final answer:

The converse, inverse, and contrapositive of the given conditional statement 'If 2+2=4, then h=1' are 'If h=1, then 2+2=4', 'If 2+2≠4, then h≠1', and 'If h≠1, then 2+2≠4', respectively. The biconditional is '2+2=4 if and only if h=1'.

Step-by-step explanation:

The question involves creating different logical statements based on a given conditional statement, a concept rooted in mathematical logic. If we consider the statement 'If 2+2=4, then h=1', we can create its converse, inverse, and contrapositive. Also, we can determine its biconditional form.

Converse

The converse of a statement switches the hypothesis and conclusion. So the converse of the given statement is 'If h=1, then 2+2=4'.

Inverse

The inverse of a statement negates both the hypothesis and the conclusion. Therefore, the inverse is 'If 2+2≠4, then h≠1'.

Contrapositive

The contrapositive negates and switches the hypothesis and conclusion. The contrapositive is 'If h≠1, then 2+2≠4'.

Biconditional

The biconditional essentially combines the original statement and its converse, indicating that both conditions are necessary and sufficient for each other. The biconditional is '2+2=4 if and only if h=1'.

User Arntor
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