Question

Total number of ordered pairs in universal relation for set B= {α,β, gamma, delta} is _____


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Answer 1

Given :  Set B = { α , β , γ , δ)

To Find : Total number of ordered pairs

Solution:

Set B = { α , β , γ , δ)

There are 4 elements

a pair have 2 elements

2 elements out  of 4 can be selected in ⁴C₂  = 6 ways

And its given that ordered pair hence order of elements also matter hence each pair can be arranged in 2 ways

Hence total number of ordered pairs in universal relation for set B= { α , β , γ , δ)  are  2 * 6  = 12

Here is the list

{ ( α , β) , (α, γ) , (α , δ ) , ( β ,α) , (β, γ) , (β , δ ) , (  γ , β) , (γ, α) , (γ , δ ) , ( δ ,α) , (δ,β) , (δ , δ ) }

12 number of ordered pairs

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Answer 2

Given:-

$\sf{B = \{\alpha, \: \beta , \: \gamma , \: \delta} \}$

To find:-

total number of ordered pairs.

Solution:-

$\sf{B = \{\alpha, \: \beta , \: \gamma , \: \delta} \}$

» there are four elements

» a pair have two elements

» 2 elements out of 4 can be selected in

$\bf^{4} C_{2} = 6 \: ways$

» and it's given that ordered pairs hence ordered of elements also matters hence which pair can be arranged in two ways.

Hence, total number of ordered pairs in

Universal relation for set B = {α, β, ץ, δ}

are 2×6 = 12

Here is the list :

{ (α, β) , (α,ץ) , (α, δ) , ( β,α) , ( β, ץ) , ( β, δ) , ( ץ, β,) , (ץ, α) , (ץ, δ) , ( δ, α) , ( δ,β) , ( δ, δ)

12 number of ordered pairs