Advertisements
Advertisements
Question
Let A = {1, 2, 3, 4} and R = {(a, b) : a ∈ A, b ∈ A, a divides b}. Write R explicitly.
Solution
Given:
A = {1, 2, 3, 4}
R = {(a, b) : a ∈ A, b ∈ A, a divides b}
We know:
1 divides 1, 2, 3 and 4.
2 divides 2 and 4.
3 divides 3.
4 divides 4.
∴ R = {(1, 1), (1, 2), (1, 3), (1, 4), (2, 2), (2, 4), (3, 3), (4, 4)}
APPEARS IN
RELATED QUESTIONS
If G = {7, 8} and H = {5, 4, 2}, find G × H and H × G.
State whether the following statement is true or false. If the statement is false, rewrite the given statement correctly.
If P = {m, n} and Q = {n, m}, then P × Q = {(m, n), (n, m)}.
If A = {–1, 1}, find A × A × A.
Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that A × (B ∩ C) = (A × B) ∩ (A × C)
Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that 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.
If A = {1, 2} and B = {1, 3}, find A × B and B × A.
If A = {1, 2, 3} and B = {2, 4}, what are A × B, B × A, A × A, B × B and (A × B) ∩ (B × A)?
If A and B are two set having 3 elements in common. If n(A) = 5, n(B) = 4, find n(A × B) and n[(A × B) ∩ (B × A)].
Let A and B be two sets. Show that the sets A × B and B × A have elements in common iff the sets A and B have an elements in common.
If A = {−1, 1}, find A × A × A.
State whether of the statement is true or false. If the statement is false, re-write the given statement correctly:
(iii) If A = {1, 2}, B = {3, 4}, then A × (B ∩ ϕ) = ϕ.
If A = {1, 2}, from the set A × A × A.
If A = {2, 3}, B = {4, 5}, C ={5, 6}, find A × (B ∪ C), A × (B ∩ C), (A × B) ∪ (A × C).
If A = {1, 2, 3}, B = {4}, C = {5}, then verify that:
(i) A × (B ∪ C) = (A × B) ∪ (A × C)
If A = {1, 2, 3}, B = {4}, C = {5}, then verify that:
(iii) A × (B − C) = (A × B) − (A × C)
If A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}, find
(ii) (A × B) ∩ (A × C)
Prove that:
(i) (A ∪ B) × C = (A × C) ∪ (B × C)
(ii) (A ∩ B) × C = (A × C) ∩ (B×C)
Find the domain of the real valued function of real variable:
(ii) \[f\left( x \right) = \frac{1}{x - 7}\]
Find the domain and range of the real valued function:
(vi) \[f\left( x \right) = \left| x - 1 \right|\]
Find f + g, f − g, cf (c ∈ R, c ≠ 0), fg, \[\frac{1}{f}\text{ and } \frac{f}{g}\] in :
(a) If f(x) = x3 + 1 and g(x) = x + 1
Let f(x) = 2x + 5 and g(x) = x2 + x. Describe (i) f + g (ii) f − g (iii) fg (iv) f/g. Find the domain in each case.
If f(x) be defined on [−2, 2] and is given by \[f\left( x \right) = \begin{cases}- 1, & - 2 \leq x \leq 0 \\ x - 1, & 0 < x \leq 2\end{cases}\] and g(x)
\[= f\left( \left| x \right| \right) + \left| f\left( x \right) \right|\] , find g(x).
Let A = {1, 2, 3, 4} and B = {5, 7, 9}. Determine B × A
Let A = {–1, 2, 3} and B = {1, 3}. Determine B × A
Let A = {–1, 2, 3} and B = {1, 3}. Determine B × B
Let A = {–1, 2, 3} and B = {1, 3}. Determine A × A
State True or False for the following statement.
If A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}, then (A × B) ∪ (A × C) = {(1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 3), (3, 4), (3, 5), (3, 6)}.
State True or False for the following statement.
If A × B = {(a, x), (a, y), (b, x), (b, y)}, then A = {a, b}, B = {x, y}
The number of elements in the set {x ∈ R: (|x| –3)|x + 4| = 6} is equal to ______.
