Which of the following statements has the same truth value as the statement "if it is friday, then bruce has beans for supper."? if it is not friday, then bruce does not have beans for supper. if bruce has beans for supper, then it is friday. if bruce does not have beans for supper, then it is not friday.

The contrapositive of the statement p ⇒ q is not q ⇒ not p and both the statements are equivalent.

So, the contrapositive of the statement "If it is Friday, then Bruce has beans for supper" is "If Bruce does not have beans for supper, then, it is not Friday"

This is the last statement given and is the answer.

the last one is the answer

Step-by-step explanation:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for