If X and Y are two sets such that X cup Y has | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) It is given that:$n(X \cup Y) = 18, n(X) = 8, n(Y) = 15$We know the formula for the number of elements in the union of two sets:$n(X \cup Y) = n(X

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(A) It is given that:$n(X \cup Y) = 18, n(X) = 8, n(Y) = 15$We know the formula for the number of elements in the union of two sets:$n(X \cup Y) = n(X) + n(Y) - n(X \cap Y)$Substituting the given values into the formula:$18 = 8 + 15 - n(X \cap Y)$$18 = 23 - n(X \cap Y)$Rearranging to solve for $n(X \cap Y)$:$n(X \cap Y) = 23 - 18$$n(X \cap Y) = 5$Therefore,the number of elements in $X \cap Y$ is $5$.

If $X$ and $Y$ are two sets such that $X \cup Y$ has $18$ elements,$X$ has $8$ elements,and $Y$ has $15$ elements,how many elements does $X \cap Y$ have?

Similar Questions

If $A=\{1, 2, 3, 4\}, B=\{3, 4, 5, 6\}, C=\{5, 6, 7, 8\}$ and $D=\{7, 8, 9, 10\}$,find $A \cup C$.

Which of the following pairs of sets are disjoint?
${1, 2, 3, 4}$ and ${x : x \text{ is a natural number and } 4 \le x \le 6}$

If $P, Q$ and $R$ are subsets of a set $A$,then $R \times (P^c \cup Q^c)^c =$

If $A = \{x \in R : |x| < 2\}$ and $B = \{x \in R : |x - 2| \geq 3\}$,then:

Find the union of each of the following pairs of sets:
$X = \{1, 3, 5\}, Y = \{1, 2, 3\}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module