You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XI

Mathematics

Graphical Interpretation of Continuity

State whether...

Question

State whether each of the following statements are true or false. If the statements is false, re-write the given statements 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 ∈ B and y ∈ A.
(iii) If A = {1, 2}, B = {3, 4}, then A × (B ∩ ϕ) = ϕ.

Open in App

Solution

(i) False
Correct statement:
If P = {m, n} and Q = {n, m}, then P × Q = {(m, n), (m, m), (n, n), (n, m)}.

(ii) False
Correct statement:
If A and B are non-empty sets, then A × B is a non-empty set of an ordered pair (x, y) such that x ∈ A and y ∈ B.

(iii) True
A = {1, 2} and B = {3, 4}
Now,
(B ∩ ϕ) = ϕ
The Cartesian product of any set and an empty set is an empty set.
∴ A × (B ∩ ϕ) = ϕ

Suggest Corrections

Similar questions

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 $A \times (B \cap ϕ) = ϕ$

Q. State whether each of the following statements are true or false. If the statement is false, rewrite the given statement correctly.

(i)

P = {m, n}

and

Q = {n, m}

, then

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

(i i)

A

and

B

are non-empty sets, then

A \times B

is a non-empty set of ordered pairs

(x, y)

such that

x \in A

and

y \in B

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

, then

A \times (B \cap ϕ) = ϕ

Q. State whether each of the following statements 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 \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 \in A

and

y \in B

(iii) If

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

then

A \times (B \cap ϕ) = ϕ

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.

Q. Let

A, B

are two non-empty sets and

U

be the universal set. Then which of the following statements is/are true?

1. n (A \cup B)^{'} = n (A^{'} \cap B^{'})

2.

A \cap B = ϕ,

then

A^{'} \cup B^{'} = U

3.

A \cup B = U,

then

A^{'} \cap B^{'} = ϕ

4.

A \subset B,

then

A^{'} \cup B^{'} = (A \cap B)^{'}

(where

ϕ

denote the null set)

Join BYJU'S Learning Program