Let A = 1 , 2 , 3 , 4 , 5 , 6 , 7 . Define B = T ⊆ A : either 1 ∉ T or 2 ∈ T and C = T ⊆ A : T the sum of all the elements of T is a prime number. Then the number of elements in the set B ∪ C is _______.

Question

Let A = 1 , 2 , 3 , 4 , 5 , 6 , 7 . Define B = T &#8838; A : either 1 &#8713; T or 2 &#8712; T and C = T &#8838; A : T the sum of all the elements of T is a prime number. Then the number of elements in the set B &#8746; C is _______.

Quantrex Academy · Accepted Answer

Correct answer: 0

We know that, By demorgan's law B &#8746; C ' = B ' &#8745; C ' B ' is a set containing sub sets of A containing element 1 and not containing 2 . And C ' is a set containing subsets of A whose sum of elements is not prime. So, we need to calculate number of subsets of 3 , 4 , 5 , 6 , 7 whose sum of elements plus 1 is composite. Number of such 5 elements subset = 1 Number of such 4 elements subset = 3 (except selecting 3 or 7 ) Number of such 3 elements subset = 6 (except selecting 3 , 4 , 5

Let A = 1 , 2 , 3 , 4 , 5 , 6 , 7 . Define B = T ⊆ A : either 1 ∉ T or 2 ∈ T and C = T ⊆ A : T the sum of all the elements of T is a prime number. Then the number of elements in the set B ∪ C is _______.

Correct answer

Step-by-step solution

More from Sets and Relations

Let A = 1 , 2 , 3 , 4 , 5 , 6 , 7 . Define B = T &#8838; A : either 1 &#8713; T or 2 &#8712; T and C = T &#8838; A : T the sum of all the elements of T is a prime number. Then the number of elements in the set B &#8746; C is _______.

Correct answer

Step-by-step solution

More from Sets and Relations

Let A = 1 , 2 , 3 , 4 , 5 , 6 , 7 . Define B = T ⊆ A : either 1 ∉ T or 2 ∈ T and C = T ⊆ A : T the sum of all the elements of T is a prime number. Then the number of elements in the set B ∪ C is _______.