Advertisements
Advertisements
प्रश्न
Let A = {1, 2, 3, 4} and B = {5, 7, 9}. Determine is A × B = B × A?
उत्तर
Since A = {1, 2, 3, 4} and B = {5, 7, 9}.
Therefore, No, A × B ≠ B × A.
Since A × B and B × A do not have exactly the same ordered pairs.
APPEARS IN
संबंधित प्रश्न
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)}.
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.
If A = {1, 2} and B = {1, 3}, find A × B and B × A.
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, 3}, B = {4}, C = {5}, then verify that:
(i) A × (B ∪ C) = (A × B) ∪ (A × C)
If A × B ⊆ C × D and A × B ≠ ϕ, prove that A ⊆ C and B ⊆ D.
Find the domain of the real valued function of real variable:
(i) \[f\left( x \right) = \frac{1}{x}\]
Find the domain of the real valued function of real variable:
(iii) \[f\left( x \right) = \frac{3x - 2}{x + 1}\]
Find the domain of the real valued function of real variable:
(v) \[f\left( x \right) = \frac{x^2 + 2x + 1}{x^2 - 8x + 12}\]
Find the domain of the real valued function of real variable:
(ii) \[f\left( x \right) = \frac{1}{\sqrt{x^2 - 1}}\]
Find the domain of the real valued function of real variable:
(iv) \[f\left( x \right) = \frac{\sqrt{x - 2}}{3 - x}\]
Find the domain and range of the real valued function:
(ii) \[f\left( x \right) = \frac{ax - b}{cx - d}\]
Find the domain and range of the real valued function:
(iii) \[f\left( x \right) = \sqrt{x - 1}\]
Find the domain and range of the real valued function:
(iv) \[f\left( x \right) = \sqrt{x - 3}\]
Find the domain and range of the real valued function:
(v) \[f\left( x \right) = \frac{x - 2}{2 - x}\]
Find the domain and range of the real valued function:
(x) \[f\left( x \right) = \sqrt{x^2 - 16}\]
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
Find f + g, f − g, cf (c ∈ R, c ≠ 0), fg, \[\frac{1}{f}\text{ and } \frac{f}{g}\] in :
(b) If \[f\left( x \right) = \sqrt{x - 1}\] and \[g\left( x \right) = \sqrt{x + 1}\]
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.
Let A = {1, 2, 3, 4} and B = {5, 7, 9}. Determine A × B
Let A = {–1, 2, 3} and B = {1, 3}. Determine B × A
Let A = {–1, 2, 3} and B = {1, 3}. Determine A × A
If P = {x : x < 3, x ∈ N}, Q = {x : x ≤ 2, x ∈ W}. Find (P ∪ Q) × (P ∩ Q), where W is the set of whole numbers.
A = {x : x ∈ W, x < 2} B = {x : x ∈ N, 1 < x < 5} C = {3, 5} find A × (B ∩ C)
