Answer:
a P(x) = Q(x)
b. R(x) = Q(x)
c. R(x) = P(x)
d. Yes
Step-by-step explanation:
This is a statement of logical connectives.
a P(x) = Q(x)
b. R(x) = Q(x)
c. R(x) = P(x)
d. Yes, (c) follows from (a) and (b)
Reasoning:
(c) is equivalent to ∀x ¬ P(x) ∨ Q(x)
Proof:
Follow the tautology (X→Υ) Ξ(¬x∨Υ)
This gives X: R(x) ∧ ¬ P(X)
is the required function.
<u>Step-by-step explanation:</u>
We have to find the transformation after the horizontal and vertical shifts and then reflection over the x-axis for the given function.

If there is a horizontal shift of 3, then the function becomes, 
If there is a vertical shift of -2, then the function becomes, 
The function is reflected over the x- axis then the function becomes,

Answer:
283 cm³
Step-by-step explanation:
Given, h=10cm
r=3cm
Volume= π×r²h
=3.14×3×3×10
=282.6
Rounding off, = 283 cm³
Answer: a) 783 ways; b) 593775 ways
Step-by-step explanation:
a) Your friend wants to select 3 zinfandel out of 9 from the supply in a particular order, which means:



= 783
In the dinner party, the friend will have 783 ways of serving the zinfandel.
b) Now, your friend want to select 6 bottles out of 30 in no particular order and randomly selected. So:



= 593775
If you select 6 bottles randomly from 30, you will have 593775 ways of doing it.