Subjective Type

Let $$X = \{n \in N : 1 \le n \le 50\}.$$ If $$A = \{n \in X : n$$ is a multiple of $$2\}$$ and $$B = \{n \in X : n$$ is a multiple of $$7\}$$, then the number of elements in the smallest subset of X containing both A and B is _____.

Solution

$$X = \{x : 1 \le x \le 50 , \, x \in N\}$$ $$A = \{x : x$$ is multiple of $$2\}$$ $$\therefore n(A) = 25$$ $$B = \{x : x$$ is multiple of $$7\}$$ $$\therefore n(B) = 7$$ $$n(A \cap B) = 3$$ From question $$n(A \cup B) = n(A) + n(B) - n (A \cap B)$$ $$ = 25 + 7 - 3$$ $$ = 29$$

SIMILAR QUESTIONS

Sets, Relations and Functions

The equation x + cosx $$=$$ a has exactly one positive root. Complete set of values of 'a' is

Sets, Relations and Functions

In a combined test in English and Physics; $$36\%$$ candidates failed in English; $$28\%$$ failed in Physics and $$12\%$$ in both; find the total number of candidates appeared, if $$208$$ candidates have failed.

Sets, Relations and Functions

In a combined test in Maths and Chemistry. $$84\%$$candidates passed in Maths, $$76\%$$ in Chemistry and $$8\%$$ failed in both. If $$340$$ candidates passed in the test, then how many appeared ?

Sets, Relations and Functions

Let $$P = \left \{\theta : \sin \theta - \cos \theta = \sqrt {2} \cos \theta \right \}$$ and $$Q = \left \{\theta : \sin \theta + \cos \theta = \sqrt {2}\sin \theta \right \}$$ be two sets. Then:

Sets, Relations and Functions

If $$ \xi=\{1,2,3, \ldots .9\}, A=\{1,2,3,4,6,7,8\} $$ and $$ B=\{4,6,8\}, $$ then find. (i) $$ A^{\prime} $$ (ii) $$ B^{\prime} $$ (iii) $$ A \cup B $$ (iv) $$ \mathrm{A} \cap \mathrm{B} $$ (v) $$ A-B $$ (vi) $$ B-A $$ (vii) $$ (A \cap B)^{\prime} $$ (viii) $$ A^{\prime} \cup B^{\prime} $$ Also verify that: (a) $$ (A \cap B)^{\prime}=A^{\prime} \cup B^{\prime} $$ (b) $$ n(A)+n\left(A^{\prime}\right)=n(\xi) $$ (c) $$ n(A \cap B)+n\left((A \cap B)^{\prime}\right)=n(\xi) $$ (d) $$ n(A-B)+n(B-A)+n(A \cap B)=n(A \cup B) $$

Sets, Relations and Functions

If $$ \xi=\{x: x \in W, x \leq 10\}, A .=\{x: x \geq 5\} $$ and $$ B=\{x: 3 \leq x<8\}, $$ then verify that: $$ A-B=A \cap B^{\prime} $$

Sets, Relations and Functions

If $$ \xi=\{x: x \in W, x \leq 10\}, A .=\{x: x \geq 5\} $$ and $$ B=\{x: 3 \leq x<8\}, $$ then verify that: $$ B-A=B \cap A^{\prime} $$

Sets, Relations and Functions

If $$ n(\xi)=40, n\left(A^{\prime}\right)=15, n(B)=12 $$ and $$ n\left((A \cap B)^{\prime}\right)=32, $$ find : (i) n(A) (ii) $$ n\left(B^{\prime}\right) $$ (iii) $$ n(A \cap B) $$ (iv) $$ n(A \cup B) $$ (v) $$ n(A-B) $$ (vi) $$ n(B-A) $$

Sets, Relations and Functions

$$(P\cap Q)' \cup R$$

Contact Details