This is my first time learning descrete mathmetics and havin

This is my first time learning descrete mathmetics and having really hard time with some problems.

number 4, 9, and 12.

Anyone help?

4a.

Yes 2 is an element of the set containing the only number 2

4b. THere is only one element 2 in the set. As in the set repeating is meaningless

4c.There are two elements 0 and {0}

4d. Yes {0} is an element of the set {{0},{1}}

4e. No 0 is not an element of the set set {{0},{1}}

9.a Yes 3 belongs to {1,2,3}

b.No 1 is an element of the set {1} but not the subset

c. No {2} is not an element of {1,2} as it is a subset of the same set

d. Yes {3} is an element of {1,{2},{3}}

e. yes 1 is a element of {1}

f. No {2} is an element of {1,{2},{3}}, but not its subset.

g. Yes {1} is a subset of {1,2}

h. No 1 is not an element of {{1},2}

i. Yes {1} is a subset of {1,{2}}

j Yes {1} is a subset of {1}

12.

S={2,4,6} and T={1,3,5}

a. By defnition of cross product of two sets

SxT={(x,y)| x in S and y in T }

={(2,1),(2,3),(2,5),(4,1),(4,3),(4,5),(6,1),(6,3),(6,5)}

Number of elements is 9

b. By defnition of cross product of two sets

TxS={(x,y)| x in T and y in S }

={(1,2),(1,4),(1,6),(3,2),(3,4),(3,6),(5,2),(5,4),(5,6)}

Number of elements is 9

By defnition of cross product of two sets

SxS={(x,y)| x in S and y in S }

={(2,2),(2,4),(2,6),(4,2),(4,4),(4,6),(6,2),(6,4),(6,6)}

Number of elements is 9

By defnition of cross product of two sets

TxT={(x,y)| x in T and y in T }

={(1,1),(1,3),(1,5),(3,1),(3,3),(3,5),(5,1),(5,3),(5,5)}

Number of elements is 9