If T = {prime numbers} and M = {odd numbers} are subsets of $\mu$  = {x : 0 < x ≤ 10} and x is an integer, find (T$^{\prime}$ n M$^{\prime}$).

Step 1: List the universal set μ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Step 2: List T and M

• T (primes) = {2, 3, 5, 7}
• M (odd numbers) = {1, 3, 5, 7, 9}

Step 3: Find the complements

• T′ = elements not in T = {1, 4, 6, 8, 9, 10}
• M′ = elements not in M = {2, 4, 6, 8, 10}

Step 4: Find the intersection T′ ∩ M′ These are the elements common to both sets:

• 1 is in T′ but not in M′ (it is odd).
• 4, 6, 8, 10 are in both.
• 9 is in T′ but not in M′ (it is odd).
• 2 is in M′ but not in T′ (it is prime).

T′ ∩ M′ = {4, 6, 8, 10}

Check using De Morgan's law: T′ ∩ M′ = (T ∪ M)′ T ∪ M = {1, 2, 3, 5, 7, 9}, so its complement is {4, 6, 8, 10}. ✓

Answer: A. {4, 6, 8, 10}.

Tip: T′ ∩ M′ means "neither prime nor odd." The only numbers that are not prime and not odd are the even numbers that are not 2, which gives 4, 6, 8, 10. Also remember that 1 is not prime, but it is odd, so it gets excluded here.