Equivalence Class

Q. the number of ways in which 10 identical objects of one kind 10 of another kind and 10 of third kind can be divided between two persons so that each person has 15 objects is

Q. 28. If A={1, 2, 3}, then how many equivalence relation can be defined on A containing (1, 2) - (a) 2 (b) 3 (c) 8 (d) 6

Q.

How many equivalence classes can be formed on a deck of cards, with respect to the relation "Belongs to the same suit"

1. 13

2. 52

3. 4

4. 26

Q. Express the recurring decimal 0.1576(bar on 576) as a rational no. Using concept of infinite geometric series.?

Q. Let $A=\{x$ $\in Z:0\le x\le 12\},$ $R=\left\{\right(a,b):a,b\in A,|a-b|\text{is divisible by}4\}$, then which among the following options are correct

1. equivalence class of $1$ is $\{1,5,9\}$
2. $R$ is reflexive and symmetric but not transitive relation.
3. $R$ is a Transitive relation
4. equivalence class of $1$ is $A$

Q.

If relation R is defined as "Is of the same color" on set of objects. Then the total number of equivalence classes on the set with respect to R is equal to.

1. Number of distinct objects in the set.

2. Number of distinct colors in the set

3. (Number of objects)${}^2$

4. (Number of distinct colors)${}^2$

Q. Let W be the set of whole nos. and N the set of natural nos. , a belongs to N such that
aW={ ax : x belongs to W}

1. Describe the set 3W intersection 7W
2. Describe the set 5W intersection 15W

Q. From the sets given below, pair the equivalent sets:
$A=\left\{1,2,3\right\},B=\left\{t,p,q,r,s\right\},C=\left\{\alpha ,\beta ,\gamma \right\},D=\left\{a,e,i,o,u\right\}.$