Question #303547

“If compound X is boiling, then its temperature must be at least 150◦C.” Assuming that this

statement is true, which of the following must also be true?

a. If the temperature of compound X is at least 150◦C, then compound X is boiling.

b. If the temperature of compound X is less than 150◦C, then compound X is not boiling.

c. Compound X will boil only if its temperature is at least 150◦C.

d. If compound X is not boiling, then its temperature is less than 150◦C.

e. A necessary condition for compound X to boil is that its temperature be at least 150◦C.

f. A sufficient condition for compound X to boil is that its temperature be at least 150◦C.


1
Expert's answer
2022-02-28T14:02:21-0500

Let p be "compound X is boiling", q be "temperature must be at least 150◦C". Then statement “If compound X is boiling, then its temperature must be at least 150◦C.” can be written as p    qp\implies q

(a) q    pq\implies p is not equivalent to p    qp\implies q , so it's false

(b) ¬q    ¬p\neg q\implies \neg p is equivalent to p    qp\implies q , so it's true

(с) p    qp\iff q is not equivalent to p    qp\implies q , so it's false

(d) ¬p    ¬q\neg p\implies \neg q is not equivalent to p    qp\implies q , so it's false

(e) p    qp\implies q is equivalent to p    qp\implies q , so it's true

(f) q    pq\implies p is not equivalent to p    qp\implies q , so it's false


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