Let A = {–1, 2, 3} and B = {1, 3}. Determine B × A - Mathematics

Let A = {–1, 2, 3} and B = {1, 3}. Determine B × A

योग

Given that: A = {– 1, 2, 3} and B = {1, 3}

B × A = {(1, – 1), (3, – 1), (1, 2), (3, 2), (1, 3), (3, 3)}

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अध्याय 2: Relations and Functions - Exercise [पृष्ठ २७]

अध्याय 2 Relations and Functions
Exercise | Q 1.(ii) | पृष्ठ २७

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)}.

State whether the following statement is true or false. If the statement is false, rewrite the given statement correctly.

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.

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

Let A = {1, 2, 3, 4} and R = {(a, b) : a ∈ A, b ∈ A, a divides b}. Write R explicitly.

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:

If P = {m, n} and Q = {n, m}, then P × Q = {(m, n), (n, m)}

Given A = {1, 2, 3}, B = {3, 4}, C ={4, 5, 6}, find (A × B) ∩ (B × 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)

If A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}, find

(iv) (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:

(i) \[f\left( x \right) = \frac{1}{x}\]

Find the domain of the real valued function of real variable:

(iii) \[f\left( x \right) = \sqrt{9 - x^2}\]

Find the domain of the real valued function of real variable:

(iv) \[f\left( x \right) = \frac{\sqrt{x - 2}}{3 - x}\]