Finite Math Question?

Question

Let R = {x,t }, S = {q,t,y }, and T = {t,p,y,v,x },

1.) y ∈ S ∩ T?

2.) x ∈ S ∩ T?

What does this actually mean? Is Y the element of S and intersects T? an or The elements of S intersect T? if so #1 is False, and #2 is True... Could someone give clarification. I am not understanding my book.

Answer 1

umm, i can help you with this...but if you could tell me how you got the contained in and interesection symbols i would appreciate it

ok...we are told that R is the set of elements x and t
and we are told S is the set of elements q, t, and y
and T is the set of elements t,p,y,v, and x

so part 1 asks
is y contained in the intersection of S and T, in other words is y in both S and T, it is, so its true

in part 2, we are asked is x contained in the intersection fo S and T, well that asks is x in both set S and set T, its not, so x is not in the intersection, so its false

hope this helps
matttlocke

Answer 2

This means-- is y an element of the intersection of S and T. Since the intersection of S and T has the elements of S that are also elements of T, the intersection of S and T is {t,y}. y is an element of that intersection. Since x is only in T, it's not in the intersection of S and T.

So, #1 is true, #2 is false.

Answer 3

1) y ∈ S ∩ T just means that

y is an element of S *and* y is an element of T. As you can see, it's true (looking at the sets S and T).

2) x ∈ S ∩ T means

x is an element of S *and* x is an element of T. Although x is an element of S, x is NOT an element of T, rendering the statement false.

If we wanted to, we can assign S ∩ T to a set which we can name B. Then, S ∩ T are the elements common to both, and

S ∩ T = {t, y}

Answer 4

S ∩ T means "all members that S and T have in common".

(Intersection (∩) is a binary operation on two sets, and the result is itself a set.)

Therefore, S ∩ T is the set { t, y }

1) Yes, y is a member of the set S ∩ T = { t, y }

2) No, x is not a member of the set S ∩ T = { t, y }

Answer 5

∩ means the operation which denotes the set having elements common to S and T

Now figure it out.