Let X= 1,2,3,4,5 . The number of different ordered pairs (Y, Z) that can be formed such that Y ⊆ X, Z ⊆ X and Y ∩ Z is empty, is

Question

Let X= 1,2,3,4,5 . The number of different ordered pairs (Y, Z) that can be formed such that Y ⊆ X, Z ⊆ X and Y ∩ Z is empty, is (A) 52 (B) 35 (C) 25 (D) 53

Tardigrade Admin · Accepted Answer

Here, X= 1,2,3,4,5 Now, the possibilities are (i) 1 ∈ Y, 1 ∈ Z (ii) 1 ∈ Y, 1 ∉ Z (iii) 1 ∉ Y, 1 ∈ Z (iv) 1 ∉ Y, 1 ∉ Z (ii) (iii) ,(iv) are favourable cases for Y ∩ Z to be empty. Similarly , for other elements we have 3 favourable cases. ∴ Required number of different ordered pairs (Y, Z)=3 × 3 × 3 × 3 × 3=35

Q. Let $X = {1, 2, 3, 4, 5}$ . The number of different ordered pairs $(Y, Z)$ that can be formed such that $Y \subseteq X, Z \subseteq X$ and $Y \cap Z$ is empty, is

$5^{2}$

$3^{5}$

$2^{5}$

$5^{3}$

Q. Let X={1,2,3,4,5}. The number of different ordered pairs (Y,Z) that can be formed such that Y⊆X,Z⊆X and Y∩Z is empty, is

52

35

25

53

Q. Let $X = {1, 2, 3, 4, 5}$ . The number of different ordered pairs $(Y, Z)$ that can be formed such that $Y \subseteq X, Z \subseteq X$ and $Y \cap Z$ is empty, is

$5^{2}$

$3^{5}$

$2^{5}$

$5^{3}$