Out of 500 car owners investigated, 400 owned car A and 200 owned car B, 50 owned both A and B cars. Is this data correct?

If K = {a,b,d e f }  L = {b,c,d,g} and M = {a,b,c,d,h}, then find the following:
(i) K \(\cup \)(L \(\cap \) M)
(ii) K \(\cap \)(L \(\cup \) M)
(iii) (K\(\cup \)L)\(\cap \)(K\(\cup \)M)
(iv) (K\(\cap \)L)\(\cup \)(K\(\cap \)M)

Verify \(A-(B\cap C)=(A-B)\cup (A-C)\)using Venn diagrams.

If U = {4,7,8,10,11,12,15,16}, A = {7,8,11,12,} and B = {4,8,12,15}, then verify De Morgan’s Laws for complementation.

Verify \((A\cap B)'=A'\cup B'\) using Venn diagrams.

In the adjacent diagram, if n(U) = 125, y is two times of x and z is 10 more than x, then find the value of x,y and z.

If P = {x : x\(\in \)W and 0 < x < 10} Q = {x : x = 2n+1, n\(\in \)W and n < 5} and R = {2, 3, 5, 7, 11, 13}  then verify P −(Q ⋂ R) = (P − Q) U (P − R).

In a college, 240 students play cricket, 180 students play football, 164 students play hockey, 42 play both cricket and football, 38 play both football and hockey, 40 play both cricket and hockey and 16 play all the three games. If each student participate in atleast one game, then find
(i) the number of students in the college
(ii) the number of students who play only one game.

In a group of 100 students, 85 students speak Tamil, 40 students speak English, 20 students speak French, 32 speak Tamil and English, 13 speak English and French and 10 speak Tamil and French. If each student knows atleast any one of these languages, then find the number of students who speak all these three languages.

If A = {-2,0,1,3,5}, B = {-1,0,2,5,6} and C = {-1,2,5,6,7} then show that A-(BUC) = (A-B)∩(A-C).