Question

if 3^x=9^y-1 and 16^3-x=8^y-2 then x-y
a) 56/11
b) 4/11
c) 7/11
d) 26/11

Answer 1

Answer:

A={3,5,7,9,11},B={7,9,11,13},C={11,13,15} and D={15,17}

(i) A∩B={7,9,11}

(ii) B∩C={11,13}

(iii) A∩C∩D=(A∩C)∩D={11}∩{15,17}=ϕ

(iv) A∩C={11}

(v) B∩D=ϕ

(vi) A∩(B∪C)=(A∩B)∪(A∩C)

={7,9,11}∪{11}={7,9,11}

(vii) A∩D=ϕ

(viii) A∩(B∪D)=(A∩B)∪(A∩D)

={7,9,11}∪ϕ={7,9,11}

(ix) (A∩B)∩(B∪C)={7,9,11}∩{7,9,11,13,15}={7,9,11}

(x) (A∪D)∩(B∪C)={3,5,7,9,11,15,17}∩{7,9,11,13,15}

={7,9,11,15}

thank you