The weight of an elephant is 100 times the weight of a cat. If the elephant weighs 14,000 pounds, how many pounds does the cat w
2 answers:
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Answer:
a. True
b. False
c. True
d. False
Step-by-step explanation:
a. Meaning
as we can see that x is an element of Y
So notation is
Therefore x is the subset of Y if each of an element of X is also an element of Y.
So notation is
2. (a) We need to proof
When
We will say that A, B and C are the set that is
When A = ∅ then which shows true, as the set of empty is a subset of each set.
Hence, it is safe to say that A is not the empty set.
Now we will proof directly
Let us say x be an element of A
As each of the element of A is also an element of B
As , each if the element of B is also an element of C
Therefore, as we can see that each of an element of A is also known an element of C, that states
So, the given statement is true, as we conclude with a proof.
(b). We will assume {1}, B = {{1},2} and C = {{1},2,3}
As in the point a, which is an element of B, that is which is true
As all of the elements in B are also an element in C, which is also correct.
Although, is false as 1 is an element of A that is not in C.
(c) We need to proof
When then
Let us assume that A, B and C are the sets that
As,
As, , each of the element of B is also an element of C
So, its true.
(d) We will assume {1}, B = {{1},2} and C = {{1},2,3}
As in the point a, which is an element of B, that is which is true
As {{1},2} is an element of B, is correct
Although is not correct as {1) is not an element in C.
SO the statement is false