Equivalence Class

Q.

Mac has three daughters. He gives 4x, 6y, and 9z marbles to his three daughters. The daughters observe that the number of the marbles with each one of them is the same.

What is the relation between x, y, and z?

1. 

2. 

3. 

4. 

Q. The change required for sentence underlined at [7] is?

1. In addition
2. For example
3. NO CHANGE
4. Certainly

Q. R be a relation in a set A. Then R is an equivalence relation in A if and only if _____________________________.

1. R is reflexive, R is symmetric and R is transitive
2. R is antireflexive, R is symmetric and R is transitive
3. R is antireflexive, R is antisymmetric and R is transitive
4. None of the above

Q. Let P = {x | x is a letter in the word 'CATARACT'} and Q = {y | y is a letter in the word 'TRAC'}
show that the P = Q.

Q. If $\overline{x}$ is mean of $x_1,x_2..........x_n,$ then prove that if a is added to each term then mean will be $(\overline{x}+a)$