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

MCQ_SINGLE
Out of all the patients in a hospital 89% are found to be suffering from heart ailment and 98% are suffering from lungs infection. If K% of them are suffering from both ailments, then K can not belong to the set :
NUMERICAL
The number of relations on the set $A=\{1,2,3\}$, containing at most 6 elements including $(1,2)$, which are reflexive and transitive but not symmetric, is __________.
NUMERICAL
Let $A=\{1,2,3,4\}$ and $R=\{(1,2),(2,3),(1,4)\}$ be a relation on $\mathrm{A}$. Let $\mathrm{S}$ be the equivalence relation on $\mathrm{A}$ such that $R \subset S$ and the number of elements in $\mathrm{S}$ is $\mathrm{n}$. Then, the minimum value of $n$ 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 :
MCQ_SINGLE
Let $A = {-3, -2, -1, 0, 1, 2, 3}$. Let R be a relation on A defined by $xRy$ if and only if $0 \le x^2 + 2y \le 4$. Let $l$ be the number of elements in R and $m$ be the minimum number of elements required to be added in R to make it a reflexive relation. Then $l + m$ is equal to
View All Questions