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Complex Numbers

State whether...

Question

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 ∩ Φ) = Φ.

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Solution

(i) False

If P = {m, n} and Q = {n, m}, then

P × Q = {(m, m), (m, n), (n, m), (n, n)}

(ii) True

(iii) True

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Similar questions

(i)

P = {m, n}

Q = {n, m}

P \times Q = {(m, n), (n, m)}

(i i)

A

B

A \times B

(x, y)

x \in A

y \in B

(i i i) A = {1, 2}, B = {3, 4}

A \times (B \cap ϕ) = ϕ

P = {m, n}

Q = {n, m}

P \times Q = {(m, n), (n, m)}

A

B

A \times B

(x, y)

x \in A

y \in B

A = {1, 2}, B = {3, 4}

A \times (B \cap ϕ) = ϕ

State whether each of the following statements are true or false. If the statement is false, re-write the given statement correctly

(i) If P = {m, n} and Q = {n, m}. then $P \times Q =$ {(m, n), (n, m)}

(ii) If A and B are non-empty sets, then $A \times B$ is a non - empty set of ordered pairs (x, y) such that $x ϵ B$ and $y ϵ A .$

(iii) If A = {1, 2}, B = {3, 4}, then $A \times (B \cap ϕ) = ϕ$

Question 51

State whether the given statement is True or False.

If $\frac{p}{q}$ is a rational number and m is a non-zero integer then $\frac{p}{q} = \frac{p \times m}{q \times m}$

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