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Sets, Relations and Functions

Let $A$ be a non-empty set such that $A \times A$ has $9$ elements among which are found $(- 1, 0)$ and $(0, 1)$ , then

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Sets, Relations and Functions

Given,
$A = {b, c, d}$ and $B = {x, y}$ : find element of $A \times B$ .

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Sets, Relations and Functions

Suppose $S = {1, 2}$ and $T = {a, b}$ then $T \times S$

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Sets, Relations and Functions

If $G = {7, 8}$ and $H = {5, 4, 2}$ , find $G \times H$ and $H \times G$ .

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Sets, Relations and Functions

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 $A \times (B \cap ϕ) = ϕ$

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Sets, Relations and Functions

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 $A \times B$ find $A$ and $B$ where $x, y$ and $z$ are distinct elements

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Sets, Relations and Functions

The cartesian product $A \times A$ has $9$ elements among which are found $(- 1, 0)$ and $(0, 1)$ . Find the set $A$ and the remaining elements of $A \times A$