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3 years ago

Use a truth table to show that P Qand (~PV Q) A (~QV P) are equivalen

Mathematics

1 answer:

kati45 [8]3 years ago

8 0

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).

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While on a business trip to Brookfield, Haley treated her co-workers to a meal that cost $50. Haley knew that when the bill came

frosja888 [35]

Answer:

$66

Step-by-step explanation:

The meal cost $50 without taxes.

The cost of tax:

$50*%14= $7

so she will pay a $7 tax

Also, she wants to tip %18 of the original $50 so:

$50*%18= $9

so she will tip $9

$50 + $7 + $9 = $66

8 0

3 years ago

Shani borrowed $5000 at an annual interest rate of 4% compounded yearly. William borrowed the same amount of money at an annual

Natalka [10]

Answer: William will pay $ 330.76 more interest than Shani at the end of 3 years.

Step-by-step explanation:

Compound interest = $P((1+r)^t-1)$ <em> , </em>P= principal , r= rate of interest , t= time

Given: P = $5000 , t= 3 years

For Shani , r= 4% = 0.04

Compound interest = $5000((1+0.04)^3-1)$

$=5000(1.124864-1)\\\\=5000(0.124864)\\\\=\$\ 624.32$

For William, r= 6%= 0.06

Compound interest = $5000((1+0.06)^3-1)$

$=5000(1.191016-1)\\\\=5000(0.191016)\\\\=\$\ 955.08$

Difference = $ ( 955.08- 624.32)

= $ 330.76

Hence, William will pay $ 330.76 more interest than Shani at the end of 3 years.

6 0

3 years ago

What about this one?????

nikitadnepr [17]

Answer:

B) {14,7}

Step-by-step explanation:

If the x-axis increases by 2 and the y-axis increases by 1 then think of it as the y-axis will always be HALF of the x-axis. In this case, 7 is half of 14 (14÷2=7). :)

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2 years ago

Please help me on this will give you brainliest

elena-14-01-66 [18.8K]

7 1/4, 8.209, 8.22, 83/10

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2 years ago

(80pts) The ratio of the number of A's in the class to B's in the class was 2:5. How many people got A's if there were 40 people

allsm [11]

Make a proportion using the ratio (A:B) given and number of As and Bs really gotten in the class ( $\frac{A's}{B's}$ )

$\frac{2}{5} = \frac{A}{40}$

Cross multiply

2 * 40 = 5 * A

80 = 5A

Isolate A by dividing 5 to both sides

80/5 = 5A/5

16 = A

If 40 people in the class got B's then 16 people got A's

Hope this helped!

~Just a girl in love with Shawn Mendes

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2 years ago