COMEDK 2025 Afternoon Solved Paper

Concept:Find elements of sets $A$ and $B$, then their union. Identify primes in the union and count them.Explanation:Step 1: Set $A = \{x : x = 4n+1, n \in \mathbb{Z}, 0 \le n < 4\}$. Possible $n$: $0, 1, 2, 3$. So $A = \{1, 5, 9, 13\}$.Step 2: Set $B = \{x : x = 15n+4, n \in \mathbb{N}, n \le 3\}$. Natural numbers start from $1$, so $n = 1, 2, 3$. Thus $B = \{19, 34, 49\}$.Step 3: Union $A \cup B = \{1, 5, 9, 13, 19, 34, 49\}$.Step 4: Identify primes in the union. $1$ is not prime. $5$ is prime. $9$ is not prime. $13$ is prime. $19$ is prime. $34$ and $49$ are not prime. So primes are $\{5, 13, 19\}$.Step 5: Thus $C = \{5, 13, 19\}$. Cardinal number $|C| = 3$.Answer:$3$ (Option B).