Let X = {x : 1 ≤ x ≤ 50, x ∈ N}A = {x: x is multiple of 2}B...
X={x:1 less than or equal to x less than or equal to50,x belongs to natural number(N)},---(given),
A={x:x is a multiple of 2}={2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,....50},
nA=a=2,d=2,an=50,
an=a+(n-1)d,
50=2+(n-1)2,
48/2=n-1,
24+1=n,
n=25,
or, nA=25,
B={x:x is a multiple of 7},
={7,14,21,28,35,42,49},
nB=7,
AintersectionB ={14,28,42},n (AUB)=3,
Now, to find--> the number of elements in the smallest subset of x which contains both the element of a and b=n(A UB),
n(AUB)=nA+nB -n(A intersection B),
=25+7-3=29