If A- B-a-1-a-2-a-3-b-1-b-2-b-3- then nA - nB - -

Given that A× B={(a,1),(a,2),(a,3),(b,1),(b,2),(b,3)}. ⇒ A =Set of all first coordinates of A× B= {a, b} and B =Set of all second coordinates of A× B = {1, 2, 3 ...

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Standard XIII

Mathematics

Cartesian Product

If A× B=a,1,a...

Question

If $A \times B = {(a, 1), (a, 2), (a, 3), (b, 1), (b, 2), (b, 3)},$ then $n (A) + n (B) =$ .

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Solution

The correct option is B 5
Given that $A \times B = {(a, 1), (a, 2), (a, 3), (b, 1), (b, 2), (b, 3)} .$
$\Rightarrow A = Set of all first coordinates of A \times B$ $= {a, b}$
and $B = Set of all second coordinates of A \times B$
$= {1, 2, 3}$
$\Rightarrow n (A) + n (B) = 2 + 3 = 5$

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Similar questions

Q. If

A \times B = {(a, 1), (a, 2), (a, 3), (b, 1), (b, 2), (b, 3)},

then

n (A) + n (B) =

Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (x, 1), (y, 2), (z, 1) are $A \times B,$ write A and B.

Match the following:

Given U is universal set.

A, B are subsets of U.

n(U), n(A), n(B) are no. of elements in U, A, B respectively.

Number of:

(1) Elements neither in A nor in B (A) $n (A \cup B)$

(2) Elements only in A (B) $n (B) - n (A \cap B)$

(3) Elements only in B (C) $n (A) - n (A \cup B)$

(4) Elements either in A (or) in B (D) $n (U) - n (A \cup B)$

(E) $n (A) - n (A \cap B)$

Q. If

n (A) = 3, n (B) = 5, n (A \cap B) = 2

, find

n (A \cup B)

Q. Verify n (A

\cup

\cup

C) = n (A) + n(B) + n (C) – n(A

\cap

B) – (B

\cap

C) – n(A

\cap

C) + (A

\cap

\cup

C) for the following sets A = {1, 3, 5, 6, 8}, B = {3, 4, 5, 6} and C = {1, 2, 3, 6}

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If A×B={(a,1),(a,2),(a,3),(b,1),(b,2),(b,3)}, then n(A)+n(B)= .

The correct option is B 5Given that A×B={(a,1),(a,2),(a,3),(b,1),(b,2),(b,3)}. ⇒A=Set of all first coordinates of A×B={a,b} and B=Set of all second coordinates of A×B ={1,2,3} ⇒n(A)+n(B)=2+3=5

If $A \times B = {(a, 1), (a, 2), (a, 3), (b, 1), (b, 2), (b, 3)},$ then $n (A) + n (B) =$ .

The correct option is B 5
Given that $A \times B = {(a, 1), (a, 2), (a, 3), (b, 1), (b, 2), (b, 3)} .$
$\Rightarrow A = Set of all first coordinates of A \times B$ $= {a, b}$
and $B = Set of all second coordinates of A \times B$
$= {1, 2, 3}$
$\Rightarrow n (A) + n (B) = 2 + 3 = 5$