1. The set $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$ is the set of counting numbers up to 10. 2. The set $C$ is the set of multiples of 3 less than 10, so $C = \{3, 6, 9\}$. The element of $C$ from the options is 6. 3. $A$ is even numbers from 1 to 10: $A = \{2, 4, 6, 8, 10\}$. $B$ is odd numbers from 1 to 10: $B = \{1, 3, 5, 7, 9\}$. $A \cup B$ means union, which is all elements from $A$ or $B$, which is $U$. 4. $A \cap B$ means intersection, which are elements common to both $A$ and $B$. Being even and odd sets, $A \cap B = \emptyset$. 5. Cardinality $|U|$ means number of elements in $U$. Since $U$ contains 1 to 10, $|U| = 10$. 6. $C'$ is complement of $C$, elements in $U$ but not in $C$. So $C' = \{1, 2, 4, 5, 7, 8, 10\}$. 7. Subset of $B$ must contain only odd numbers from 1 to 10. $\{3, 5\}$ is such subset. 8. Disjoint sets have no elements in common. Between $A$ (even) and $B$ (odd), they share no elements, so $A$ and $B$ are disjoint. 9. $C - A$ means elements in $C$ but not in $A$. Since $C = \{3,6,9\}$ and $A = \{2,4,6,8,10\}$, $C - A = \{3,9\}$. 10. $(A \cup B) \cap C = U \cap C = C$. 11. From the Venn diagram, $A \cap B = \{1, 4\}$. 12. Cardinality of $U$ is total elements in $U$: counting 9,16,25,1,4,6,2,3,8,12,30,7,26 gives 13. 13. $(A \cup B)'$ means elements not in $A \cup B$ inside $U$ = $\{7, 12, 26, 30\}$. 14. Statement B is true: $A$ is the set of perfect squares of numbers 1 to 5, i.e., $9,16,25$. 15. The set $\{9,16,25\}$ is $A - B$. 16. $A \cup B'$ means elements in $A$ or not in $B$. Since $B = \{6,2,3,8\}$, $B'$ is numbers not in $B$, so elements like 9 are in this union. 17. $B - A = \{6, 8, 3, 2\}$. 18. Set B is the set of positive factors of 24 less than 10: $\{6,2,3,8\}$ fits this. 19. $B \cap A'$ has 4 elements: 6, 2, 3, 8. 20. $B \cap A = \{1,4\}$ has 2 elements, so number of subsets is $2^{2} = 4$. 21. $N$ is natural numbers, typically starting from 1, so 0 is NOT in $N$. 22. $W \cap Z$ means elements common to whole numbers and integers, which is $W$. 23. $N \cup Q$ means union of natural numbers and rational numbers, which is $Q$. 24. Statement C is true: $N \subseteq Q$ (natural numbers are subset of rational). 25. Irrational number is $\pi$. 26. $W \setminus N$ is whole numbers not in natural numbers, that is $\{0\}$. 27. $Z$ in roster form is integers: $\{...,-3,-2,-1,0,1,2,3,...\}$. 28. All listed sets are subsets of $Q$, so answer is none of the above. 29. $W \cap N = N$. 30. $Q \cup Z = Q$. Final answers: 1:A 2:C 3:D 4:A 5:C 6:D 7:B 8:A 9:C 10:C 11:B 12:C 13:C 14:B 15:C 16:A 17:B 18:C 19:C 20:D 21:A 22:A 23:B 24:C 25:D 26:B 27:A 28:D 29:C 30:B