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Anestetic [448]
3 years ago
11

I WILL MARK BRAINLIST Which problem can be solved by performing this multiplication? 3/4×8/9

Mathematics
1 answer:
Lana71 [14]3 years ago
3 0
The answer is 4/9

Have a great day!!
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Let A, B, C and D be sets. Prove that A \ B and C \ D are disjoint if and only if A ∩ C ⊆ B ∪ D
ANEK [815]

Step-by-step explanation:

We have to prove both implications of the affirmation.

1) Let's assume that A \ B and C \ D are disjoint, we have to prove that A ∩ C ⊆ B ∪ D.

We'll prove it by reducing to absurd.

Let's suppose that A ∩ C ⊄ B ∪ D. That means that there is an element x that belongs to A ∩ C but not to B ∪ D.

As x belongs to A ∩ C, x ∈ A and x ∈ C.

As x doesn't belong to B ∪ D, x ∉ B and x ∉ D.

With this, we can say that x ∈ A \ B and x ∈ C \ D.

Therefore, x ∈ (A \ B) ∩ (C \ D), absurd!

It's absurd because we were assuming that A \ B and C \ D were disjoint, therefore their intersection must be empty.

The absurd came from assuming that A ∩ C ⊄ B ∪ D.

That proves that A ∩ C ⊆ B ∪ D.

2) Let's assume that A ∩ C ⊆ B ∪ D, we have to prove that A \ B and C \ D are disjoint (i.e.  A \ B ∩ C \ D is empty)

We'll prove it again by reducing to absurd.

Let's suppose that  A \ B ∩ C \ D is not empty. That means there is an element x that belongs to  A \ B ∩ C \ D. Therefore, x ∈ A \ B and x ∈ C \ D.

As x ∈ A \ B, x belongs to A but x doesn't belong to B.  

As x ∈ C \ D, x belongs to C but x doesn't belong to D.

With this, we can say that x ∈ A ∩ C and x ∉ B ∪ D.

So, there is an element that belongs to A ∩ C but not to B∪D, absurd!

It's absurd because we were assuming that A ∩ C ⊆ B ∪ D, therefore every element of A ∩ C must belong to B ∪ D.

The absurd came from assuming that A \ B ∩ C \ D is not empty.

That proves that A \ B ∩ C \ D is empty, i.e. A \ B and C \ D are disjoint.

7 0
3 years ago
What is the value of 1.2^2
sveticcg [70]
Value of 1.2^2=1.44
value of 2^3+17-3*4=8+17-12=13
value of 9^2/3^3= 81/27=3
7 0
2 years ago
The product if the following numbers is evenly divided by what numbers 737×74
IceJOKER [234]
737 X 74 = 54,538
Evenly divided by: 2, 11, and 22
6 0
3 years ago
Carly is on her senior soccer team. She makes 42% of her foul shots, leading her team to 16 wins in 18 games for season. If Carl
STALIN [3.7K]
The answer is D. You just need to multiply .42x71.hope this helped you out!!!
4 0
3 years ago
ms. Cho bought 1/3 yard of wool and 5/8 of oil. the wool cost $9 per yard and the silk $12 per yard. how much did Ms. Cho spend
iren [92.7K]
Wool = $3
Silk = $7.5
So $10.50 in total.
Hope it helps!
3 0
2 years ago
Read 2 more answers
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