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4 years ago

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

Mathematics

1 answer:

kati45 [8]4 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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Solve the inequality 5x7 < 2x - 1

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x is strictly less than 2 or x ∈ (-∞, 2)

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Inequalities are statements that are represented as comparison between two or more numbers or algebraic expressions.(strictly less, strictly great, greater, lesser)

Solving the given equation:

5x - 7 < 2x - 1

=> 5x - 7 - 2x < 2x - 1 - 2x

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The number line is attached below.

Know more about "inequalities" here: brainly.com/question/20383699

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Disclaimer: The given question is incomplete. The complete question is given below.

Solve the inequality 5x - 7 < 2x - 1

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1 year ago

If (x-2,6)=(4,y+2)then the value of x=_____and y=____

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Step-by-step explanation:

( x-2,6)=(4,Y+2)

this means; (x-2) &( 4) stands for" x "axis.

and( 6 )& (y+2) stands for y axis.

So, we can say( x-2)=X1 & (4)=X2 , (6)=Y1 & (y+2)=Y2

then; to Solve The Equation we use The Formula: X1=X2 for "X" And Y1=Y2 for "Y".

Solution: for "X" ; X1=X2

x-2= 4

x=4+2

x=<u>6</u>

For "Y" ; Y1=Y2

6 = y+2

y=6-2

y=<u>4</u>

finally check ; ( (x-2),6) = (4,(y+2) )

(6-2),6 = (4,(4+2) )

( (4),6) = (4,(6) )

(4,6) = (4,6)

so, X1 =X2 ; 4 = 4

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