Class JEE Mathematics Sets, Relations, and Functions Q #1070
KNOWLEDGE BASED
APPLY
4 Marks 2012 AIEEE 2012 MCQ SINGLE
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:
(A) $3^5$
(B) $2^5$
(C) $5^3$
(D) $5^2$
Prev Next
Correct Answer: A
Explanation
For any element $x_i$ present in $X$, 4 cases arise while making subsets $Y$ and $Z$.

Case 1: $x_i \in Y, x_i \in Z \implies Y \cap Z \neq \emptyset$

Case 2: $x_i \in Y, x_i \notin Z \implies Y \cap Z = \emptyset$

Case 3: $x_i \notin Y, x_i \in Z \implies Y \cap Z = \emptyset$

Case 4: $x_i \notin Y, x_i \notin Z \implies Y \cap Z = \emptyset$

Therefore, for every element, the number of ways is $3$ for which $Y \cap Z = \emptyset$.

Thus, the total number of ways is $3 \times 3 \times 3 \times 3 \times 3 = 3^5$ since the number of elements in set $X$ is $5$.

More from this Chapter

NUMERICAL
Let S = {1, 2, 3, 5, 7, 10, 11}. The number of non-empty subsets of S that have the sum of all elements a multiple of 3, is _____________.
NUMERICAL
Let $A = \sum\limits_{i = 1}^{10} {\sum\limits_{j = 1}^{10} {\min \,\{ i,j\} } } $ and $B = \sum\limits_{i = 1}^{10} {\sum\limits_{j = 1}^{10} {\max \,\{ i,j\} } } $. Then A + B is equal to _____________.
NUMERICAL
The number of elements in the set $\{ n \in Z:|{n^2} - 10n + 19| < 6\} $ is _________.
MCQ_SINGLE
The relation $R = \{(a, b) : gcd(a, b) = 1, 2a \neq b, a, b \in Z\}$ is:
MCQ_SINGLE
Let $R = \{(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)\}$ be a relation on the set $A = \{3, 6, 9, 12\}$. The relation is :
View All Questions