Answer:
1:>
2:>
3:>
Step-by-step explanation:
A goes with number 3. B goes with number 4. C goes with number 6. D goes with number 5. E goes with number 2. F goes with number 7. G goes with number 1.
Given:
P = Set of all triangles,
Q = Set of scalene triangles,
R = Set of isosceles triangles and
S = Set of equilateral triangles.
To find:
Which of the following statements are true or false?
Solution:
We know that,
Scalene triangles : All sides are different.
Isosceles triangles : Two sides are equal.
equilateral triangles : All sides are equal.
Set of all triangles contains all scalene triangles. So, set of scalene triangles Q is a subset of Set of all triangles P.

So, (a) is true.
All isosceles triangles are not equilateral triangles. So, set of isosceles triangles R is not a subset of set of equilateral triangles S.

So, (b) is false.
Set of all isosceles triangles contains all equilateral triangles. So, set of equilateral triangles S is a subset of set of isosceles triangles R .

So, (c) is true.
Answer:
Step-by-step explanation:
1st expression: x⁴-y⁴
= (x²)² - (y²)²
= (x² +y²)(x² -y²)
= (x² +y²)(x +y)(x -y)
= (x +y)(x -y)(x² +y²)
2nd expression: x² -y²
= (x +y)(x -y)
3rd expression: x³ -y³
= (x -y)(x² +xy +y²)
Now ,
Lowest Common Multiples (L.C.M.) = common factors * rest factors
= (x+y)(x-y) * (x² +y²)(x² +xy +y²)
= (x² -y²)(x²+y²) * (x² +xy +y²)
= (x⁴ -y⁴)(x² +xy +y²)
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