Let A = 1,2,3,4,5,6,7 and B = 3,6,7,9 . Then the number of elements in the set C ⊆ A: C ∩ B ≠ φ is

Question

Let A = 1,2,3,4,5,6,7 and B = 3,6,7,9 . Then the number of elements in the set C ⊆ A: C ∩ B ≠ φ is  (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

A = 1,2,3,4,5,6,7 and B = 3,6,7,9 Total subset of A =27=128 C ∩ B =φ when set C contains the element 1,2,4,5 ∴ S= C ⊆ A ; C ∩ B ≠ φ = operatornameTotal-( C ∩ B =φ) =128-24=112

Q. Let $A = {1, 2, 3, 4, 5, 6, 7}$ and $B = {3, 6, 7, 9}$ . Then the number of elements in the set ${C \subseteq A : C \cap B \neq = ϕ}$ is _______

$A = {1, 2, 3, 4, 5, 6, 7}$ and
$B = {3, 6, 7, 9}$
Total subset of $A = 2^{7} = 128$
$C \cap B = ϕ$ when set $C$ contains the element
$1, 2, 4, 5$
$∴ S = {C \subseteq A; C \cap B \neq = ϕ}$
$= Total - (C \cap B = ϕ)$
$= 128 - 2^{4} = 112$

Q. Let A={1,2,3,4,5,6,7} and B={3,6,7,9}. Then the number of elements in the set {C⊆A:C∩B=ϕ} is _______

A={1,2,3,4,5,6,7} and B={3,6,7,9} Total subset of A=27=128 C∩B=ϕ when set C contains the element 1,2,4,5 ∴S={C⊆A;C∩B=ϕ} =Total−(C∩B=ϕ) =128−24=112

Q. Let $A = {1, 2, 3, 4, 5, 6, 7}$ and $B = {3, 6, 7, 9}$ . Then the number of elements in the set ${C \subseteq A : C \cap B \neq = ϕ}$ is _______

$A = {1, 2, 3, 4, 5, 6, 7}$ and
$B = {3, 6, 7, 9}$
Total subset of $A = 2^{7} = 128$
$C \cap B = ϕ$ when set $C$ contains the element
$1, 2, 4, 5$
$∴ S = {C \subseteq A; C \cap B \neq = ϕ}$
$= Total - (C \cap B = ϕ)$
$= 128 - 2^{4} = 112$