Answer: The given logical equivalence is proved below.
Step-by-step explanation: We are given to use truth tables to show the following logical equivalence :
P ⇔ Q ≡ (∼P ∨ Q)∧(∼Q ∨ P)
We know that
two compound propositions are said to be logically equivalent if they have same corresponding truth values in the truth table.
The truth table is as follows :
P Q ∼P ∼Q P⇔ Q ∼P ∨ Q ∼Q ∨ P (∼P ∨ Q)∧(∼Q ∨ P)
T T F F T T T T
T F F T F F T F
F T T F F T F F
F F T T T T T T
Since the corresponding truth vales for P ⇔ Q and (∼P ∨ Q)∧(∼Q ∨ P) are same, so the given propositions are logically equivalent.
Thus, P ⇔ Q ≡ (∼P ∨ Q)∧(∼Q ∨ P).
Step-by-step explanation:
I don't know if the first set of numbers is all in one set, but I'll do my best to give you an answer.
Really all you need to do is use PEMDAS for the first question.
(Parentheses, exponents, multiply, divide, add, subtract. In that order)
Then to simplify that fraction next to it, notice that 0.018 is 3x 0.06.
that's a 3:1 ratio, so it ends up simplifying to this:
Lastly, to solve the division of that fraction. If you divide by a fraction, you multiply whatever it's dividing by its inverse.
So...
Idk if she's too young to learn cross multiply, but this is an easier method.
Multiply everything by 4 which cancels out the 4 on the left side.
36z-16/5 <= 7z + 2
Now multiply everything by 5, cancelling out the right side 5.
36z-16 <= 35z + 10
Solve the equation normally
z-16<=10
z<=36
It is 2 12/20 simplified is 2 6/10 simplified is 2 3/5
So if you want it simplified it is 2 6/10 but if you just want the answer I think it would be 2 3/5
Hope this is helpful
And have a great day
2-x+3=16 is the answer. good luck?
