Question

If U ={x | x ∈ N, x < 10} and A = {x | x ∈ N, 2 ≤ x < 6} then (A′)′ is

Answer 1

Answer:

.

Step-by-step explanation:

Given sets are:-

U ={x | x ∈ N, x < 10}

=>U={1,2,3,4,5,6,7,8,9}

and A = {x | x ∈ N, 2 ≤ x < 6}

=>A={2,3,4,5,6}

Now, A'=U-A

=>A'={1,2,3,4,5,6,7,8,9} - {2,3,4,5,6}

=>A'= {1,7,8,9}

and (A')'= U- A'

=>(A')'=>{1,2,3,4,5,6,7,8,9} - {1,7,8,9}

=>(A')'= {2,3,4,5,6}

=>A

Therefore, (A')'=A

Answer 2

Concept:

A set is a collection of well defined elements or objects. A set is denoted by a capital letter, and the cardinal number of a set is enclosed in a curly bracket to indicate how many members there are in a finite set. Set A, for instance, is a collection of all the natural numbers, with the form A = 1, 2, 3, 5, 6, 7, 8, etc.

Given:

If U ={x | x ∈ N, x < 10} and A = {x | x ∈ N, 2 ≤ x < 6}

Find:

then (A′)′ is

Solution:

Given sets are:-

U ={x | x ∈ N, x < 10}

=>U={1,2,3,4,5,6,7,8,9}

and A = {x | x ∈ N, 2 ≤ x < 6}

=>A={2,3,4,5,6}

Now, A'=U-A

=>A'={1,2,3,4,5,6,7,8,9} - {2,3,4,5,6}

=>A'= {1,7,8,9}

and (A')'= U- A'

=>(A')'=>{1,2,3,4,5,6,7,8,9} - {1,7,8,9}

=>(A')'= {2,3,4,5,6}

=>A

Therefore, (A')'=A

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