Use the rules of inference to prove the conclusion r given (all 1,2,3 and 4) the four premises listed below. Write your solution
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Answer:
Here we will use the relationships:
And a number:
is between 0 and 1 if a is positive and larger than 1, and n is negative.
if a is positive and 0 < a < 1, then we need to have n positive such that:
0 < a^n < 1
A)
This is between zero and 1,
B)
This is greater than 1, because the exponent is positive.
C)
Because a is smaller than 1, and the exponent is positive, then the expression is between 0 and 1.
D)
The exponent is negative (and pair) then the expression is between 0 and 1.
Remember that when the exponent is pair, we always have that:
(-N)^m = (N)^m
So (-7)^-2 = 7^-2