consider u = {x|x is a real number}. a = {x|x ∈ u and x + 2 > 10} b = {x|x ∈ u and 2x > 10} which pair of…

consider u = {x|x is a real number}. a = {x|x ∈ u and x + 2 > 10} b = {x|x ∈ u and 2x > 10} which pair of statements is correct? 5 ∉ a; 5 ∈ b 6 ∈ a; 6 ∉ b 8 ∉ a; 8 ∈ b 9 ∈ a; 9 ∉ b

consider u = {x|x is a real number}. a = {x|x ∈ u and x + 2 > 10} b = {x|x ∈ u and 2x > 10} which pair of statements is correct? 5 ∉ a; 5 ∈ b 6 ∈ a; 6 ∉ b 8 ∉ a; 8 ∈ b 9 ∈ a; 9 ∉ b

Answer

Answer:

C. $8\notin A; 8\in B$

Explanation:

Step1: Solve for set A

Solve $x + 2>10$. Subtract 2 from both sides: $x>8$. So $A={x|x\in U,x > 8}$.

Step2: Solve for set B

Solve $2x>10$. Divide both sides by 2: $x > 5$. So $B={x|x\in U,x>5}$.

Step3: Check each option

  • For 5: Since $5\ngtr8$, $5\notin A$; since $5\ngtr5$, $5\notin B$.
  • For 6: Since $6\ngtr8$, $6\notin A$; since $6>5$, $6\in B$.
  • For 8: Since $8\ngtr8$, $8\notin A$; since $8>5$, $8\in B$.
  • For 9: Since $9>8$, $9\in A$; since $9>5$, $9\in B$.