Relations Test ...

Let N denote the set of all natural numbers. Define two binary relations on N as $$R_1=\{(x, y)\epsilon N\times N : 2x+y=10\}$$ and $$R_2=\{(x, y)\epsilon N\times N:x+2y=10\}$$. Then.

Consider the following two binary relations on the set $$A = \left \{a, b, c\right \} : R_{1} = \left \{(c, a), (b, b), (a, c), (c, c), (b, c), (a, a)\right \}$$
and $$R_{2} = \left \{(a, b), (b, a), (c, c), (c, a), (a, a), (b, b), (a, c)\right \}$$ Then

Let  $$S = \{ 1,2,3 , \ldots , 100 \} .$$  The number of non-empty subsets  $$A$$  of  $$S$$  such that the product of elements in  $$A$$  is even is :-

$$A$$ and $$B$$ are two sets having $$3$$ and $$4$$ elements respectively and having $$2$$ elements in common. The number of relations which can be defined from $$A$$ to $$B$$ is:

Let $$R$$ be a relation from a set $$A$$ to a set $$B$$, then:

If $$A = \{x, y\}$$ and $$B = \{3, 4, 5, 7, 9\}$$ and $$C = \{4, 5, 6, 7\}$$, find $$\displaystyle A\times (B\cap C)$$

$$\displaystyle x^{2} = xy$$ is a relation (defined on set R) which is
 

Which one of the following relations on R (set of real numbers) is an equivalence relation 

If $$\displaystyle A\prime $$ is symmetric to A and $$\displaystyle B\prime $$ is symmetric to B with respect to a line of symmetry, then