A -B - C-A- A-B -A-CB- A-B -A-CC- A-B - CD- A-B - C

The correct option is A (A B)∩ (A C)We have A (B∪ C)=(A B)∩ (A C)—(1) Let us use Venn diagrams in understanding this. Consider three sets A, B and C. Then, The ...

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Standard IX

Mathematics

Venn Diagram

A -B ∪ C=A. A...

Question

$A - (B \cup C)$ =

(A - B) \cap (A - C)

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(A - B) \cup (A - C)

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(A - B) \cup C

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(A - B) \cap C

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Solution

The correct option is A $(A - B) \cap (A - C)$
We have $A - (B \cup C) = (A - B) \cap (A - C) - - - (1)$
Let us use Venn diagrams in understanding this.
Consider three sets $A$ , $B$ and $C$ .
Then,
The third figure represents the LHS of (1).
Now, consider
and $⟹$ Thus, LHS=RHS.

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Similar questions

A - (B \cap C)

A - (B \cap C)

= _______

Q. For three sets

A, B

and

C, A \cap (B - C) =

Q. If A = {a,b}, B = {b,c} and C = {b,c,d} ; then A

\times

\cup

C) = _____ .

Q. Let

A = {1, 2, 3}, B = {3, 4}

and

C = {4, 5, 6}

. Find

(A) A \times (B \cap C)

(B) (A \times B) \cap (A \times C)

(C) A \times (B \cup C)

(D) (A \times B) \cup (A \times C)

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A−(B∪C)=

The correct option is A (A−B)∩(A−C)We have A−(B∪C)=(A−B)∩(A−C)−−−(1) Let us use Venn diagrams in understanding this. Consider three sets A, B and C. Then, The third figure represents the LHS of (1). Now, consider and ⟹ Thus, LHS=RHS.

$A - (B \cup C)$ =

The correct option is A $(A - B) \cap (A - C)$
We have $A - (B \cup C) = (A - B) \cap (A - C) - - - (1)$
Let us use Venn diagrams in understanding this.
Consider three sets $A$ , $B$ and $C$ .
Then,
The third figure represents the LHS of (1).
Now, consider
and $⟹$ Thus, LHS=RHS.