Fill in the blanks to make each of the following a true statement: (i) (ii) Φ′ ∩ A = … (iii) (iv)

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Solution

(i)

Let A be the set of elements of a universal set U .

A is the plane portion of the figure; therefore, A' will be shaded portion.

Hence, A∪A'=U .

(ii)

ϕ is the null set; therefore, ϕ' will be the set of all elements of universal set which are not present in ϕ .

Since, no elements are present in ϕ , therefore ϕ'=U .

Therefore, ϕ'∩A=U∩A=A

(iii)

Since no elements of A and A' are common; therefore, intersection of this will be a null set.

Therefore, A∩A'=ϕ .

(iv)

U is the universal set.

U' means no element of U .

Therefore U'=ϕ

Hence, U'∩A=ϕ

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Similar questions

Fill in the blanks to make each of the following a true statement :

(i) $A \cup A^{'} = . . . . . . . .$ (ii) $Φ^{'} \cap A = . . . . . .$

(iii) $A \cap A^{'} = . . . . . .$ (iv) $U^{'} \cap A = . . . . . .$

Fill in the blanks to make each of the following a true statement:

(i)

(ii) Φ′ ∩ A = …

(iii)

(iv)

A \cup A^{'} = . . .

ϕ^{'} \cap A = . . .

A \cap A^{'} = . . .

U^{'} \cap A = . . .

(i) A \cup A^{'} = . . . . (i i) ϕ^{'} \cap A = . . . .

(i i i) A \cap A^{'} = . . . . (i v) U^{'} \cap A = . . . .

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