Let R be a relation defined on the set $\{ 1,2,3,4\} imes \{ 1,2,3,4\}$ by$R = \{((a,b),(c,d)):2a

Question

Let R be a relation defined on the set $\{ 1,2,3,4\} 	imes \{ 1,2,3,4\}$ by$R = \{((a,b),(c,d)):2a + 3	ext{ }b = 3c + 4	ext{ }d\}$.Then the number of elements in R is

Accepted Answer

Sol. (a,b) (c,d) (1, 1) x $$(1,2)$$ x $$(1,3)$$ $$(1,2)$$ $$(1,4)$$ $$(2,2)$$ $$(2,1)$$ $$(1,1)$$ $$(2,2)$$ $$(2,1)$$ $$(2,3)$$ $$(3,1)$$ $$(2,4)$$ $$(4,1)$$ $$(3,1)$$ x $$(3,2)$$ x $$(3,3)$$ $$(1,3)$$ $$(3,4)$$ $$(2,3)$$ $$(4,1)$$ $$(1,2)$$ $$(4,2)$$ $$(2,2)$$ $$(4,3)$$ $$(3,2)$$ $$(4,4)$$ $$(4,2)$$

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More Set, Relation and Function Questions

Sol. (a,b)		(c,d)
(1, 1)		x
$$(1,2)$$		x
$$(1,3)$$		$$(1,2)$$
$$(1,4)$$		$$(2,2)$$
$$(2,1)$$		$$(1,1)$$
$$(2,2)$$		$$(2,1)$$
$$(2,3)$$		$$(3,1)$$
$$(2,4)$$		$$(4,1)$$
$$(3,1)$$		x
$$(3,2)$$		x
$$(3,3)$$		$$(1,3)$$
$$(3,4)$$		$$(2,3)$$
$$(4,1)$$		$$(1,2)$$
$$(4,2)$$		$$(2,2)$$
$$(4,3)$$		$$(3,2)$$
$$(4,4)$$		$$(4,2)$$