Answer:
See answer below
Step-by-step explanation:
The statement ‘x is an element of Y \X’ means, by definition of set difference, that "x is and element of Y and x is not an element of X", WIth the propositions given, we can rewrite this as "p∧¬q". Let us prove the identities given using the definitions of intersection, union, difference and complement. We will prove them by showing that the sets in both sides of the equation have the same elements.
i) x∈AnB if and only (if and only if means that both implications hold) x∈A and x∈B if and only if x∈A and x∉B^c (because B^c is the set of all elements that do not belong to X) if and only if x∈A\B^c. Then, if x∈AnB then x∈A\B^c, and if x∈A\B^c then x∈AnB. Thus both sets are equal.
ii) (I will abbreviate "if and only if" as "iff")
x∈A∪(B\A) iff x∈A or x∈B\A iff x∈A or x∈B and x∉A iff x∈A or x∈B (this is because if x∈B and x∈A then x∈A, so no elements are lost when we forget about the condition x∉A) iff x∈A∪B.
iii) x∈A\(B U C) iff x∈A and x∉B∪C iff x∈A and x∉B and x∉C (if x∈B or x∈C then x∈B∪C thus we cannot have any of those two options). iff x∈A and x∉B and x∈A and x∉C iff x∈(A\B) and x∈(A\B) iff x∈ (A\B) n (A\C).
iv) x∈A\(B ∩ C) iff x∈A and x∉B∩C iff x∈A and x∉B or x∉C (if x∈B and x∈C then x∈B∩C thus one of these two must be false) iff x∈A and x∉B or x∈A and x∉C iff x∈(A\B) or x∈(A\B) iff x∈ (A\B) ∪ (A\C).
Answer:
"More than" is the same as "greater than". The symbol for greater than is >
The inequality should be: c > 5
Step-by-step explanation:
The question is not well-expressed, but it looks like you want to evaluate
5 + (-3) - 65 + (-3) - 65 + (-3) - 6
Answer:
-140
Step-by-step explanation:
First of all, note the following
- Multiplying a negative number by another negative number gives a positive number.
- Multiplying a negative number by a positive number gives a negative number.
- Multiplying a positive number by a positive number gives a positive number.
- Brackets mean multiplication.
So
5 + (-3) - 65 + (-3) - 65 + (-3) - 6
= 5 - 3 - 65 - 3 - 65 - 3 - 6
= -140
Answer:
Give 3 what?
Step-by-step explanation:
I would like to help but I need more information
Answer:
2
Step-by-step explanation:
4-5= -1
13-18+2= (-5+2)= -3
-1-(-3)=2
Don't forget your order of operations
P (parenthesis)
E (exponents)
MD (multiplication/division)
AS (addition/subtraction)
