1. Problem: Determine the nature of the set $A = (2,4,6,8,10, \ldots)$. - This set contains even numbers starting from 2 and continues indefinitely. - A set with infinite elements is called an infinite set. - Therefore, $A$ is an infinite set. 2. Problem: Find the cardinality of the set $A = (3,4,5,5,6,7,8)$. - Cardinality means the number of distinct elements. - Remove duplicates: $(3,4,5,6,7,8)$. - Count elements: 6. 3. Problem: Determine the relationship between sets $L = (3,1,2)$ and $M = (1,2,3)$. - Sets are equal if they contain the same elements regardless of order. - Both sets have elements 1, 2, and 3. - Therefore, $L$ and $M$ are equal sets. 4. Problem: Identify which option is a proposition. - A proposition is a statement that is either true or false. - "8 + 4 = 12" is a statement that is true. 5. Problem: Find the truth value of $p \lor q$ if $p$ is true and $q$ is false. - $p \lor q$ means $p$ OR $q$. - True OR False is True. 6. Problem: Determine the truth value of $p \lor \neg p$. - $p \lor \neg p$ is a tautology, always true. 7. Problem: Find $A \cup B$ for $A = (1,2,3,4)$ and $B = (4,5,6,7)$. - Union combines all unique elements. - $A \cup B = (1,2,3,4,5,6,7)$. 8. Problem: Find the number of subsets of $A = (15,16,17)$. - Number of subsets of a set with $n$ elements is $2^n$. - Here, $n=3$, so subsets = $2^3 = 8$. Final answers: 1. C. Infinite 2. B. 6 3. C. Equal sets 4. B. 8 + 4 = 12 5. B. True 6. C. True 7. None of the options exactly match correct union $(1,2,3,4,5,6,7)$ 8. B. 8