Question

{1-(-1)^x} for all integral X is the set​

Answer 1

Answer:

{0,2}

Step-by-step explanation:

Taking x=2 (even number)

{1-(-1)²} = {1-1} = {0}

Taking x=3 (odd number)

{1-(-1)³} = {1+1} = {2}

{1-(-1)^x} for all integral X is the set​ {0,2}

Answer 2

Given :   1-(-1)^x   for all integral x

To Find : Set

Solution:

x is integer even or odd

x = 2n  or 2n+ 1

x = 2n

(-1)^x  

= (-1)²ⁿ  

= ((-1)²)ⁿ

= 1ⁿ  

=  1

x = 2n + 1

(-1)^x

= (-1)²ⁿ⁺¹  

=(-1)²ⁿ(-1)

= ((-1)²)ⁿ (-1)

= 1ⁿ (-1)  

=  1(-1)

= - 1

1-(-1)ˣ  = 1 - 1 = 0   or  1 - (-1)  = 2

Hence set = { 0 , 2}

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