JAMB - Mathematics (2009 - No. 9)

I.S∩T∩W=S II. S ∪ T ∪ W = W
III. T ∩ W = S
If S⊂T⊂W, which of the above statements are true?

I and II

I and III

II and III

I, II and III

If S \(\subset\) T \(\subset\) W,

S \(\cap\) T \(\cap\) W = S is true since S \(\cap\) T = S and S \(\cap\) W = S.

S \(\cup\) T \(\cup\) W = W is also true. S \(\cup\) T = T and T \(\cup\) W = W.

However, to say that T \(\cap\) W = S is not very true mathematically. Instead, it is safe to say S \(\subset\) (T \(\cap\) W).