For A = {a, b, c, d} fin P(A), the power set of A. (Compare to example 0.3.3 0n p22) For A- (a, b, c, d) find P(A), the power se
1 answer:
Answer: The required set is {∅, {a},{b},{c},{d},{a,b},{a,c},{b,c}{c,d},{b,d},{d,a},{a,b,c},{b,c,d},{a,c,d},{a,b,d},{a,b,c,d}}
Step-by-step explanation:
Since we have given that
A= { a,b,c,d}
So, n = 4
We need to find the power set of A.
Number of elements in power set of A is
So, the power set of A has 16 elements.
So, P(A) becomes {∅, {a},{b},{c},{d},{a,b},{a,c},{b,c}{c,d},{b,d},{d,a},{a,b,c},{b,c,d},{a,c,d},{a,b,d},{a,b,c,d}}
Hence, the required set is {∅, {a},{b},{c},{d},{a,b},{a,c},{b,c}{c,d},{b,d},{d,a},{a,b,c},{b,c,d},{a,c,d},{a,b,d},{a,b,c,d}}
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Answer:
Only the second and third statements are correct:
Doubling <em>r</em> quadruples the volume.
Doubling <em>h</em> doubles the volume.
Step-by-step explanation:
The volume of a cylinder is given by:
We can go through each statement and examine its validity.
Statement 1)
If the radius is doubled, our new radius is now 2<em>r</em>. Hence, our volume is:
So, compared to the old volume, the new volume is quadrupled the original volume.
Statement 1 is not correct.
Statement 2)
Using the previous reasonsing, Statement 2 is correct.
Statement 3)
If the height is doubled, our new height is now 2<em>h</em>. Hence, our volume is:
So, compared to the old volume, the new volume has been doubled.
Statement 3 is correct.
Statement 4)
Statement 4 is not correct using the previous reasonsing.
Statement 5)
Doubling the radius results in 2<em>r</em> and doubling the height results in 2<em>h</em>. Hence, the new volume is:
So, compared to the old volume, the new volume is increased by eight-fold.
Statement 5 is not correct.