Question

Find the following given the conditional statement, "if you like math, then you like science."

The hypothesis is
Th conclusion is
The converse is
The contrapositive is

Answer 1

The hypothesis is "You like math."

The conclusion is "You like science."

The converse is "If you like science, then you like math."

The contrapositive is "If you don't like science, then you don't like math."

Explanation:

A conditional statement is a logical statement that consists of an "if-then" structure, where the "if" part (hypothesis) presents a condition or circumstance, and the "then" part (conclusion) indicates the outcome or result that follows if the condition is met.

The given conditional statement is:

• "If you like math, then you like science."

Hypothesis

The hypothesis of a conditional statement is the circumstance or event upon which the outcome depends, appearing after the "if" part of the statement. Therefore:

• The hypothesis is "You like math."

Conclusion

The conclusion of a conditional statement is the outcome or result that is stated as a consequence of the hypothesis, appearing after the "then" part of the statement. Therefore:

• The conclusion is "You like science."

Converse

The converse of a conditional statement is a new statement formed by reversing the order of the original hypotheses and conclusion. Therefore:

• The converse is "If you like science, then you like math."

Contrapositive

The contrapositive of a conditional statement is a new statement formed by both reversing the order of the original hypothesis and conclusion and negating them, resulting in the opposite conditional relationship. Therefore:

• The contrapositive is "If you don't like science, then you don't like math."

Answer 2

Hypothesis: You like math.

Conclusion: You like science.

Converse: If you like science, then you like math.

Contrapositive: If you don't like science, then you don't like math.

Explanation:

The converse and contrapositive are logically equivalent to the original conditional statement, but the converse is not logically implied by the original statement, and the contrapositive is logically implied by the negation of the original statement.