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vodka [1.7K]
3 years ago
6

Find A intersection B.

Mathematics
1 answer:
Alecsey [184]3 years ago
3 0
A: {<u>1</u>, 2, 3, <u>4</u>, 5, 6, <u>7</u>, 8, 9, 10, <u>11</u>, 12}
<span>B: {-2, -1, <u>1</u>, <u>4</u>, <u>7</u>, <u>11</u>}

</span>A<span> ∩ </span>B = {1, 4, 7, 11}

So the answer is B.

Intersection of two or more sets cointains only common elements.
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How many equivalence relations are there on the set 1, 2, 3]?
Alex787 [66]

Answer:

We need to find how many number of equivalence relations are on the set {1,2,3}

A relation is an equivalence relation if it is reflexive, transitive and symmetric.

equivalence relation R on {1,2,3}

1.For reflexive, it must contain (1,1),(2,2),(3,3)

2.For transitive, it must satisfy: if (x,y)∈R then (y,x)∈R

3. For symmetric, it must satisfy: if (x,y)∈R,(y,z)∈R then (x,z)∈R

Since (1,1),(2,2),(3,3) must be there is R, (1,2),(2,1),(2,3),(3,2),(1,3),(3,1). By symmetry,

we just need to count the number of ways in which we can use the pairs (1,2),(2,3),(1,3) to construct equivalence relations.

This is because if (1,2) is in the relation then (2,1) must be there in the relation.

the relation will be an equivalence relation if we use none of these pairs (1,2),(2,3),(1,3) . There is only one such relation: {(1,1),(2,2),(3,3)}

we can have three possible equivalence relations:

{(1,1),(2,2),(3,3),(1,2),(2,1)}

{(1,1),(2,2),(3,3),(1,3),(3,1)}

{(1,1),(2,2),(3,3),(2,3),(3,2)}

6 0
3 years ago
The short sides of a rectangle are 2 inches. The long sides of the same rectangle are three less than an unknown
Brums [2.3K]

Answer:

The first student is correct

Step-by-step explanation:

With the given information there is already 4 inches on the rectangle. 13 x2 = 26. 26+4=30. For student two if the unknown number was 10 it would not work because the longest side is 3 less then the unknown number. 10-3=7. 7x2=14. 14+4= 28<30

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The area of square abcd is 7cm^2 <br><br>show that x^2+4x=3
AveGali [126]

Answer:

see explanation

Step-by-step explanation:

The area (A) of the square = s² ( s is the measure of the side )

Here s = x + 2 and A = 7 , thus

(x + 2)² = 7 ← expand left side using FOIL

x² + 4x + 4 = 7 ( subtract 4 from both sides )

x² + 4x = 3 ← as required

4 0
3 years ago
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