Sets, Relations and Functions
Of the members of three athletic teams in a school $$21$$ are in the cricket team, $$26$$ are in the hockey team and $$29$$ are in the football team. Among them, $$14$$ play hockey and cricket, $$15$$ play hockey and foot ball, and $$12$$ play foot ball and cricket. Eight play all the three games. The total number of members in the three athletic teams is
Sets, Relations and Functions
The union of the following pair of sets is:
$$A = \{2, 3, 5, 6, 7\}, B = \{4, 5, 7, 8\}$$
Sets, Relations and Functions
The union of the following pair of sets is:
$$C = \{a, e, i, o, u\}, D = \{a, b, c, d\}$$
Sets, Relations and Functions
In a class of $$140$$ students numbered $$1$$ to $$140$$, all even numbered students opted mathematics course, those whose number is divisible by $$3$$ opted Physics course and those whose number is divisible by $$5$$ opted Chemistry course. Then the number of students who did not opt for any of the three courses is?
Sets, Relations and Functions
Find the union of each of the following pairs of sets:
(i) $$X=\left \{1,3,5\right \} Y=\left \{1,2,3\right \}$$
(ii) $$A=\{a,e,i,o,u\}, B=\{a,b,c\}$$
(iii) $$A = \{x : x \mbox{ is a natural number and multiple of } 3 \}$$.
$$B = \{x : x \mbox{ is a natural number less than } 6\}$$.
(iv) $$A = \{x : x \mbox { is a natural number and } 1 < x \leq 6\}$$
$$B = \{x : x \mbox{ is a natural number and} 6 < x < 10 \}$$.
(v) $$A = \{1, 2, 3\}$$, $$B = \phi$$
Sets, Relations and Functions
Find the smallest set $$\displaystyle Y$$ such that $$\displaystyle Y\cup \left \{ 1, 2 \right \}=\left \{ 1, 2, 3, 5, 9 \right \}$$
Sets, Relations and Functions
If A and B are two sets, then
$$(A \, \cup\, B) = (A - B) \, \cup\ (B - A) \, \cup\ (A \, \cap\ B)$$