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Elden [556K]
3 years ago
14

What is equivalent to the following expression select all that apply.

Mathematics
2 answers:
STALIN [3.7K]3 years ago
8 0
C.6 3 becaue im trying to get point dont lissten to me

jok3333 [9.3K]3 years ago
8 0
<span>the equivalent to the following expression is A and C

</span>
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Given sets A and B, prove that the following two conditions are equivalent: (1) A \ B = B \ A, (2) A = B.
Jet001 [13]

Answer:

See proof below

Step-by-step explanation:

Remember that if we want to prove that two propositions P and Q are equivalent, we have to prove that P implies Q and Q implies P.

(1)→(2) Suppose that A \ B = B \ A, we will prove that A = B. Let x∈A, and for the sake of a contradiction suppose that x∉B. Then x∈A \ B by definition of difference of sets. Since A \ B = B \ A and x∈A \ B then x∈B \A, that is, x∈B and x∉A, which is a contradiction to the first assumption regarding x. Therefore x∈B, for all x∈A, which implies that A⊆B.

We can use a similar argument to prove that B⊆A, and both inclusions imply that A=B as we wanted to prove. Indeed, let x∈B, and suppose that x∉A Thus x∈B \ A. But A \ B = B \ A, then  x∈A \B, that is, x∈A and x∉B, which is absurd. Then x∈A, for all x∈B, that is, B⊆A.  

(2)→(1). Suppose that A = B. We will prove that A \ B = B \ A. By definition,  A \ B is the set of elements of A that do not belong to B. However, A=B, so A \ B is the set of elements of A that do not belon to A. There no exists such an element, since this condition is contradictory, thus A \ B=∅, the empty set. Similarly, B \ A = B \ B = ∅. The empty set is unique, therefore A \ B=∅=  B \ A.

The previous parts show that (1) and (2) are logically equivalent.

7 0
3 years ago
Help PLEASEE BRAINLIST​
Crazy boy [7]

Answer:

The first two on the right will not be used

3. goes to 1.

4. goes to 2.

5. goes to 4.

6. goes to 3.

Step-by-step explanation:

7 0
2 years ago
642 ÷ 5 standard algorithm
damaskus [11]

642/5= 128.4


i hope this helps

7 0
3 years ago
Read 2 more answers
Angle B measures 60°. What is the measure of the angle that is complementary to angle B?
vodomira [7]
Complementary angles add up to 90.
Say the complementary angle is A. 
Angle A + Angle B = 90
Angle A + 60 = 90
Angle A = 30 degrees

Hope this helps :)
6 0
3 years ago
Read 2 more answers
What is the solution to the equation? <br> x – 19 = 1
Romashka-Z-Leto [24]
+ 19 on both sides, -19 becomes 0, 1 becomes 20 x=20
3 0
3 years ago
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