Sets, Relations and Functions
The union of the following pair of sets is: $$A = \{2, 3, 5, 6, 7\}, B = \{4, 5, 7, 8\}$$
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
Given, $${ n }({ C })=21,{ n }({ H })=26,,{ n }({ F })=29$$
Also, $${ n }({ H }\cap { C })=14, { n }({ H }\cap { F })=15, { n }({ F }\cap { C })=12,{ n }({ F }\cap { C }\cap { H })=8$$
Now, $$n(C\cup F\cup H)=n(C)+n(F)+n(H)-n(C\cap F)-n(F\cap H)-n(C\cap H)+n(C\cap F\cap H)$$
$$\Rightarrow n(C\cup F\cup H)=43$$
Total number of players $$=43$$
The union of the following pair of sets is: $$A = \{2, 3, 5, 6, 7\}, B = \{4, 5, 7, 8\}$$
The union of the following pair of sets is: $$C = \{a, e, i, o, u\}, D = \{a, b, c, d\}$$
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?
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) $$A = \{1, 2, 3\}$$, $$B = \phi$$
In a committee, $$50$$ people speak French, $$20$$ speak Spanish and $$10$$ speak both Spanish and French. How many speak at least one of these two languages?
Find the smallest set $$\displaystyle Y$$ such that $$\displaystyle Y\cup \left \{ 1, 2 \right \}=\left \{ 1, 2, 3, 5, 9 \right \}$$
If A and B are two sets, then $$(A \, \cup\, B) = (A - B) \, \cup\ (B - A) \, \cup\ (A \, \cap\ B)$$