Let A be the set of primes less than 6,and B be the set of positive odd numbers less than 6. How many different sums of the form a+b are possible,if a is in A and b is in B?

We are given two sets:

• Set A consists of primes less than 6.
• Set B consists of positive odd numbers less than 6.

Now Identify the elements of sets A and B

• Set A: The primes less than 6 are 2,3,5. So, A={2,3,5}.
• Set B: The positive odd numbers less than 6 are 1,3,5. So, B={1,3,5}.

Now, We need to calculate all possible sums where a ∈ A and b ∈ B. So, we have

When a=2:

• 2+1=3
• 2+3=5
• 2+5=7

When a=3:

• 3+1=4
• 3+3=6
• 3+5=8

When a=5:

• 5+1=6
• 5+3=8
• 5+5=10

The sums we obtained are: {3, 5, 7, 4, 6, 8, 6, 8, 10}

Now, let's remove any duplicate sums. The unique sums are: {3, 4, 5, 6, 7, 8, 10}

The unique sums are 3, 4, 5, 6, 7, 8, 10. There are 7 unique sums.

Finally, The number of different sums of the form a+b is 7.