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 $B = {T \subseteq A : either 1 \notin T or 2 \in T}$ and $C = {T \subseteq A : T$ the sum of all the elements of $T$ is a prime number $}$ . Then the number of elements in the set $B \cup C$ is ______.

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Q.
Let $A = {1, 2, 3, 4, 5, 6, 7}$ . Define $B = {T \subseteq A : either 1 \notin T or 2 \in T}$ and $C = {T \subseteq A : T$ the sum of all the elements of $T$ is a prime number $}$ . Then the number of elements in the set $B \cup C$ is ______.

Ans.
(107)

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Solution

Q. 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 ______.

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Q.
Let $A = {1, 2, 3, 4, 5, 6, 7}$ . Define $B = {T \subseteq A : either 1 \notin T or 2 \in T}$ and $C = {T \subseteq A : T$ the sum of all the elements of $T$ is a prime number $}$ . Then the number of elements in the set $B \cup C$ is ______.

Ans.
(107)