a⊂e, b⊂e,\nn(a)+n(b) = 17,\nn(b)+n(a) = 23\n⇒ n(e)=?

Answer:

20

Explanation:

Step1: Recall set - theory formula

We know that (n(A)+n(A') = n(E)) and (n(B)+n(B')=n(E)). Also, (n(A)+n(B') = 17) and (n(B)+n(A')=23).

Step2: Add the two given equations

((n(A)+n(B'))+(n(B)+n(A'))=17 + 23).

Step3: Rearrange the left - hand side

((n(A)+n(A'))+(n(B)+n(B'))=40).

Step4: Substitute (n(A)+n(A') = n(E)) and (n(B)+n(B')=n(E))

(n(E)+n(E)=40).

Step5: Solve for (n(E))

(2n(E)=40), so (n(E)=\frac{40}{2}=20).