Set, Relation and FunctionHard

Question

Let R be a relation defined on the set $\{ 1,2,3,4\} \times \{ 1,2,3,4\}$ by

$R = \{((a,b),(c,d)):2a + 3\text{ }b = 3c + 4\text{ }d\}$.

Then the number of elements in R is

Options

A.6
B.18
C.12
D.15

Solution

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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