Q2 are word problems given as a sequence of hypotheses/ premises ending with "Therefore conclusion". Show that each word problem is a valid argument. Use rules of inference to show steps and reasons in the proof. 2) If interest rates increase then affordable housing is available and construction grows. Either federal loans become available or utility rates increase. Construction does not grow. If interest rates decrease then affordable housing is not available and utility rates decrease. Therefore federal loans will become available.

THIS IS A VALID ARGUMENT, because the premises "EITHER federal loan becomes available OR utility rate increase" has defined the argument to be valid if any of the premises is true, by using "either" "or"

Explanation: This argument uses "Either or" in the premises, that means one of the premises has to be true and one has to be false in the conclusion for the argument to be valid, because both of them cannot exist.

PROOF:

STEP1: define premises;

Premises 1 (P1) = Either federal loans become available

Premises 2 (P2)= utility rates increase

STEP2: define argument.

P1 or P2

That means if P1 or P2 is true that means the argument is valid, and if P1 is true, P2 has to be false. Or if P2 is true P1 has to be false.

STEP 3: check if the argument Nia valid.

From the argument "Construction does not grow. If interest rates decrease then affordable housing is not available and utility rates decrease". It is a valid argument because P2 which is true has supported the argument to be valid. Because P2 and P1 cannot be true at the same time, we can imply that since P2 which is moving in the negative direction with the argument is true, Therefore P1 should be false by moving in a counter direction with the argument.

In this argument, the conclusion is going in a negative part, that means the premises has to be in a negative part for the argument to be valid.

answer:

a

explanation: