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Representing Integers on the Number Line

Let z be the ...

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Let z be the set of all integers and A = {(a,b):a^2+3b^2 = 28,a,b belongs to z} B = {(a,b):a>b,a,b belongs to z}, then n(A intersection B)is equal to

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Z

denotes the set of all integers and

A = {(a, b) : a^{2} + 3 b^{2} = 28, a, b \in Z}

B = {(a, b) : a < b, a, b \in Z}

. Then, the number of elements in

A \cap B

Let f be the subset of Z × Z defined by f= {(ab, a+b) : a, b belongs to Z } . Is f a function from Z to Z ?

Q. Let Z be the set of integers. Show that the relation
R = {(a, b) : a, b ∈ Z and a + b is even}
is an equivalence relation on Z.

Q. The number of elements in the set

{(a, b) : 2 a^{2} + 3 b^{2} = 35, a, b \in Z}

Z

is the set of all integers is

Q. The number of elements in the set

{(a, b) / 2 a^{2} + 3 b^{2} = 35, a, b \in z}

z

is the set of all integers is

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Representing Integers on the Number Line

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