For any two sets A - B- if nA- B-100- nA-45- nB-60- then nA- B-

Given for two sets A & B n(A∪ B)=100; n(A)=45, n(B)=60 Now, we know: n(A∪ B)=n(A)+n(B) n(A∩ B) ⇒ n(A∩ B)=n(A)+n(B) n(A∪ B) ⇒ n(A∩ B)=45+60 100=5 nbsp; ...

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Standard XII

Mathematics

Cardinal Properties

For any two s...

Question

For any two sets $A & B,$ if $n (A \cup B) = 100; n (A) = 45, n (B) = 60,$ then $n (A \cap B) =$

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Solution

The correct option is A $5$
Given for two sets $A & B$
$n (A \cup B) = 100; n (A) = 45, n (B) = 60$

Now, we know:
$n (A \cup B) = n (A) + n (B) - n (A \cap B)$
$\Rightarrow n (A \cap B) = n (A) + n (B) - n (A \cup B)$
$\Rightarrow n (A \cap B) = 45 + 60 - 100 = 5$

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For any two sets A & B, if n(A∪B)=100;n(A)=45,n(B)=60, then n(A∩B)=

The correct option is A 5Given for two sets A & B n(A∪B)=100;n(A)=45,n(B)=60 Now, we know: n(A∪B)=n(A)+n(B)−n(A∩B) ⇒n(A∩B)=n(A)+n(B)−n(A∪B) ⇒n(A∩B)=45+60−100=5

For any two sets $A & B,$ if $n (A \cup B) = 100; n (A) = 45, n (B) = 60,$ then $n (A \cap B) =$

The correct option is A $5$
Given for two sets $A & B$
$n (A \cup B) = 100; n (A) = 45, n (B) = 60$

Now, we know:
$n (A \cup B) = n (A) + n (B) - n (A \cap B)$
$\Rightarrow n (A \cap B) = n (A) + n (B) - n (A \cup B)$
$\Rightarrow n (A \cap B) = 45 + 60 - 100 = 5$