1) The ordered pair (x, y) is a subset of {x, y}. Justify your answer.
2) If A={a, b, c, d} and B = {1, 2, 3} then R{(a,2), (b,1), (d, 3), (2, c)} is a relation from A to B. Justify your answer.
3) If A={a, b, c} and R is an identity relation on set A. Then the ordered pairs of R are ______________________.
4) If n(PXQ) = 200 and n(P)=100 then n(Q) =____________________.
5) Relation R= {(x, y):x>y} and x+y =8 where x,y ∈ n, then write R-1 in roster form.
6) If R = R-1 then the relation R is ________________________.
7) If A={1, 2, 3, 4, 5, 6} and B = {1, 3, 5,7} then n(AxB)_________________.
8) The domain of the relation R= {(x, y):x,y ∈ N } and x+y ≤ 9} is __________.
9) The range of the relation R= {(x, y):3x + 2y = 15} and x,y ∈ N } is __________.
10) A={x, y, z, p}; B = {7, 8, 9, 10} and a rule f is given by f(x) = 7, f(y) = 7, f(p) = 7 The relation f is a function. Justify your answer.
11) Range of the function |x - 5| is __________________________.
12) If f(x) = 2x + 3/2 then find f(3) and f(3/2)
13) Domain of the function 1/√x is ___________________________.
14) If f is a constant function and f (100) = 100, then f (2007) = ___________________
15) f: R -> R is defined by . What is f-1?
16) Let U= {1, 2, 3, 4, 5, 6, 7, 8, 9}, A={2, 4, 6, 8} and B ={2, 3, 5, 7} Verify that
I. (AUB)' = A'∩ B'
II. (A∩B)' = A'U B'
17) Let A = {x: x∈R, x≥4} and B = {x: x∈R, x<5} .Find A ∩ B?
18) If A and B are two given sets, Prove that A ∩ (A∩B)c by an example.
19) A market research group conducted a survey of 1000 consumers and reported that 720 consumers liked product A and 450 liked product B. What is the least number that must have liked both products?
20) In a survey of 25 students, it was found that 15 had taken Mathematics, 12 had taken Physics and 11 had taken Chemistry, 5 had taken Mathematics and Chemistry, 9 had taken Mathematics and Physics, 4 had taken Physics and Chemistry and 3 had taken all three subjects. Find the number of students that had taken:
a) Only Chemistry
b) Only Mathematics
c) Only Physics
d) Physics and Chemistry but not Mathematics
e) Mathematics and Physics but not Chemistry
f) Only one of the subjects
g) At least one of three subjects
h) None of three subjects
21) A survey shows that 74% of the Indians like apples, whereas 68% like oranges. What percentage of the Indians like oranges and apples?