If , find the values of x and y.

If the set A has 3 elements and the set B = {3, 4, 5}, then find the number of elements in (A × B)?

If G = {7, 8} and H = {5, 4, 2}, find G × H and H × G.

State whether each of the following statement are true or false. If the statement is false, rewrite the given statement correctly. (I) If P = {m, n} and Q = {n, m}, then P × Q = {(m, n), (n,m)}. (II) If A and B are non-empty sets, then A × B is a non-empty set of ordered pairs (x,y) such that x ? A and y ?B. (iii) If A = {1, 2}, B = {3, 4}, then A × (B n F) = F.

If A = {–1, 1}, find A × A × A.

If A × B = {(a, x), (a, y), (b, x), (b, y)}. Find A and B.

Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that (i) A × (B n C) = (A × B) n (A × C)(ii) A × C is a subset of B × D

Let A = {1, 2} and B = {3, 4}. Write A × B. How many subsets will A × B have? List them.

Let A and B be two sets such that n(A) = 3 and n (B) = 2. If (x, 1), (y, 2), (z, 1) are in A× B, find A and B, where x, y and z are distinct elements.

The Cartesian product A × A has 9 elements among which are found (–1, 0) and (0, 1). Find the set A and the remaining elements of A × A.

Let A = {1, 2, 3, … , 14}. Define a relation R from A to A by R = {(x, y): 3x – y = 0, where x, y ? A}. Write down its domain, codomain and range.

Define a relation R on the set N of natural numbers by R = {(x, y): y = x + 5, x is a natural number less than 4; x, y ? N}. Depict this relationship using roster form. Write down the domain and the range.

A = {1, 2, 3, 5} and B = {4, 6, 9}. Define a relation R from A to B by R = {(x, y): the difference between x and y is odd; x ? A, y ? B}. Write R in roster form.

The given figure shows a relationship between the sets P and Q. write this relation (i) in set-builder form (ii) in roster form. What is its domain and range?

Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by {(a, b): a, b ? A, b is exactly divisible by a}. (I) Write R in rosterform (II) Find the domain ofR (III) Find the range of R.

Determine the domain and range of the relation R defined by R = {(x, x + 5): x ? {0, 1, 2, 3, 4,5}}.

Write the relation R = {(x, x3): x is a prime number less than 10} in roster form.

Let A = {x, y, z} and B = {1, 2}. Find the number of relations from A to B.

Let R be the relation on Z defined by R = {(a, b): a, b ? Z, a – b is an integer}. Find the domain and range of R.

Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range. (i) {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)} (ii) {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)} (iii) {(1, 3), (1, 5), (2, 5)}

Find the domain and range of the following real function: (i) f(x) = –|x| (ii)

A function f is defined by f(x) = 2x – 5. Write down the values of (i) f(0), (ii) f(7), (iii) f(–3)

The function ‘t’ which maps temperature in degree Celsius into temperature in degree Fahrenheit isdefinedby.Find (i) t (0) (ii) t (28) (iii) t (–10) (iv) The value of C, when t(C) = 212

Find the range of each of the following functions. (i) f(x) = 2 – 3x, x ? R, x > 0. (I) f(x) = x² + 2, x, is a realnumber. (II) f(x) = x, x is a real number

The relation f is defined by The relation g is defined byShow that f is a function and g is not a function.

If f(x) = x2, find .

Find the domain of the function

Find the domain and the range of the real function f defined by .

Find the domain and the range of the real function f defined by f (x) = |x – 1|.

Let be a function from R into R. Determine the range of f.

Let f, g: R ? R be defined, respectively by f(x) = x + 1, g(x) = 2x – 3. Find f + g, f – g and.

Let f = {(1, 1), (2, 3), (0, –1), (–1, –3)} be a function from Z to Z defined by f(x) = ax + b, for some integers a, b. Determine a, b.

Let R be a relation from N to N defined by R = {(a, b): a, b ? N and a = b²}. Are the following true? (i) (a, a) ? R, for all a ? N (ii) (a, b) ? R, implies (b, a) ? R (iii) (a, b) ? R, (b, c) ? R implies (a, c) ? R. Justify your answer in each case.

Let A = {1, 2, 3, 4}, B = {1, 5, 9, 11, 15, 16} and f = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}. Are the following true? (i) f is a relation from A to B (ii) f is a function from A to B. Justify your answer in each case.

Let f be the subset of Z × Z defined by f = {(ab, a + b): a, b ? Z}. Is f a function from Zto Z: justify your answer.

Let A = {9, 10, 11, 12, 13} and let f: A ? N be defined by f(n) = the highest prime factor of n. Find the range of f.