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if a=(1 2 3 4) find A×A and the relation determined by (I) y=2x (II) x+y​

Sagot :

2021miss2

Answer:

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Step-by-step explanation:

A={1,2,3,4,5,6}

R={(x,y):y is divisible by x}

We know that any number (x) is divisible by itself.

(x,x)∈R

∴R is reflexive.

Now,(2,4)∈R [as 4 is divisible by 2]

But,(4,2)∈ /

R. [as 2 is not divisible by 4]

∴R is not symmetric.

Let (x,y),(y,z)∈R. Then, y is divisible by x and z is divisible by y.

∴z is divisible by x.

⇒(x,z)∈R

∴R is transitive.

Hence, R is reflexive and transitive but not symmetric.

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