Question

If U = {all positive integers} and A = {x|x ∈ U and x is an odd positive integer}, which describes Ac?

Ac = {x|x ∈ U and is an even positive integer}

Ac = {x|x ∈ U and is a negative integer}

Ac = {x|x ∈ U and is zero}

Ac = {x|x ∈ U and is not an integer}

Answer 1

ANSWER:-

GIVEN:

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U= {all positive integers}

A= {x|x€ U and x is an odd positive integer}

SOLUTION:-

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As per the question U is all positive integers. so there are no negetive integers.

That's why complement of A is =(U -- A)

As set A contains all odd positive integers so it's complement is all even positive integers. Because U contains only positive integers.

Ac={x|x€ U and is even positive integers}

[So the answer is option b]

-------××GAME CHANGER××-------

Answer 2

Ac = {x|x ∈ U and is an even positive integer}

Step-by-step explanation:

• The universal set(U) consists of only positive integers.
• Given,  A = {x|x ∈ U and x is an odd positive integer}.
• That means the set A contains all those elements which belongs to the universal set and should be a positive odd number.
• $A_{C}$ refers to the compliment of A.It means that it will contain all those elements that belong to U but does not belong to A.
• All  the positive odd integer is made up of two types of number ,i.e, positive and negative number.
• So,this set will contain all the element belonging to U and should be an even positive integer.
• Therefore,Ac = {x|x ∈ U and is an even positive integer}.