Question

Write the statement form in symbols using the conditional or the biconditional connective. name the hypothesis and the conclusion in conditional form. let p be the statement "Sally studied" and q be the statement "sally passes"

sally passes only if she studied.
A) q --> p
B) p --> q
C) p <--> q
To find the hypothesis, choose the correct answer below
A) p and q are equivelant
B) q
C) p
To find the conclusion, choose the correct answer below
A) p
B) q
C) p and q are equivelant

Answer 1

The correct representation of the statement "Sally passes only if she studied" is B) p --> q, with the hypothesis being C) p, and the conclusion being B) q. The hypothesis is the sufficient condition for the conclusion in this conditional statement.

Step-by-step explanation:

When looking at the statement "Sally passes only if she studied," this can be represented using the conditional form. In logic, a conditional is expressed in the form of "If p, then q." With p being "Sally studied" and q being "Sally passes," the correct symbolic representation of the statement is B) p --> q, which reads as "If Sally studied, then Sally passes."

The hypothesis of a conditional statement is the part that follows the "if," and the conclusion is the part that follows the "then." Therefore, for the correct answer, the hypothesis is C) p, and the conclusion is B) q.

As indicated by the conditional form, the hypothesis "Sally studied" is the sufficient condition for the conclusion "Sally passes." This relationship can also be tested empirically by examining instances where Sally studied and subsequently passed, ensuring the valid deductive inferences hold true.