Given n -U- - 20- n -A- - 12- n -B- - 9- n -A - B- - 4- where U is the universal set- A and B are subset of U- then find n -A - B-c-

Explanations for the correct option (4).Expression of universal set A and B.𝑛(A∪ B)=𝑛(A)+𝑛(B) 𝑛(A∩ B)Substitute the values.n(A∪ B)=12+9 4=17write the expression ...

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Byju's Answer

Standard XII

Mathematics

nCr Definitions and Properties

Given n (U) =...

Question

Given $n (U) = 20, n (A) = 12, n (B) = 9, n (A \cap B) = 4$ , where $\cup$ is the universal set, $A$ and $B$ are subset of $\cup$ , then $n (A \cup B^{c}) =$

$17$

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$9$

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$11$

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$3$

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$16$

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Solution

The correct option is D
$3$

Explanations for the correct option (4).
Expression of universal set $A$ and $B$ .
$n (A \cup B) = n (A) + n (B) - n (A \cap B)$
Substitute the values.
$n (A \cup B) = 12 + 9 - 4 = 17$
write the expression of $n (A \cup B^{c})$
$\begin{array}{rcl} n (A \cup B^{c}) & = & n (\cup) - n (A \cap B) \\ = & 20 - 17 \\ = & 3 \end{array}$
Therefore, the correct option is (D).

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Similar questions

Q. If

A

and

B

are subsets of the universal set

U

, then show that

i

A \subset A \cup B

A \subset B \Leftrightarrow A \cup B = B

iii

(A \cap B) \subset A

Q. If

A

and

B

are the subsets of the universal set

U

then

(A \cup B)^{'} =

____

If A and B are subsets of the universal set U, then show that,

$A \subset B \Leftrightarrow A \cup B = B$

| x |

represent number of elements in region X. Now the following conditions are given

| U | = 14

| (A - B)^{C} | = 12

| A \cup B | = 9

and

| A Δ B | = 7

, where A and B are two subsets of the universal set U and

A^{C}

represents complement of set A, then?

Q. Let

A, B

are two non-empty sets and

U

be the universal set. Then which of the following statements is/are true?

1. n (A \cup B)^{'} = n (A^{'} \cap B^{'})

2.

A \cap B = ϕ,

then

A^{'} \cup B^{'} = U

3.

A \cup B = U,

then

A^{'} \cap B^{'} = ϕ

4.

A \subset B,

then

A^{'} \cup B^{'} = (A \cap B)^{'}

(where

ϕ

denote the null set)

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Given n(U)=20,n(A)=12,n(B)=9,n(A∩B)=4, where ∪ is the universal set, A and B are subset of ∪, then n(A∪Bc)=

The correct option is D 3Explanations for the correct option (4).Expression of universal set A and B.n(A∪B)=n(A)+n(B)-n(A∩B)Substitute the values.nA∪B=12+9-4=17write the expression of n(A∪Bc)n(A∪Bc)=n∪-nA∩B=20-17=3Therefore, the correct option is (D).

Given $n (U) = 20, n (A) = 12, n (B) = 9, n (A \cap B) = 4$ , where $\cup$ is the universal set, $A$ and $B$ are subset of $\cup$ , then $n (A \cup B^{c}) =$