Let a, b r be non-empty sets. suppose that a b. suppose that b has a least upper bound. prove that a has a least upper bound, and lub a lessthanorequalto lub b.

Answer with explanation:

Given → A, B ⊆R, are non-empty sets.

Also, A ⊆ B.

It is also given that , B has least upper bound.

To Prove:→A has a least upper bound,

and → lub A ≤ lub B.

Proof:

    A and B are non empty sets.

Also, A ⊆ B

it means there are some elements in B which is not in A and there are some elements in set B which may be greater or smaller than or equal to set A.

The meaning of least upper bound is the the smallest member of the set from which all members are greater.

As, A⊆B

So, there are two possibilities ,either

→ Least upper bound set A = least upper bound set B(1)

→ Least upper bound set A < least upper bound set B(2)

Combining (1) and (2)

→→→l u b(A) ≤ l u b (B)

abde or 1,2,4, 5 is the answer

step-by-step explanation:

stew reads at the fastest rate of 265 words per minute.

step-by-step explanation:

it's a given that felicia reads at 260 word per minute and on connie's graph we can see that she reads 200 words per minute. since stew's table tells us that he read 795 in 3 minutes, we can divide 795 by 3 to find out how many words he reads per minute.

795/3 = 265

stew reads 265 words per minute - he reads at the fastest rate since felecia reads at 260 words per minute and connie reads at 200 words per minute.

stew (265) > felecia (260) > connie (200)