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rewona [7]
1 year ago
9

Activating Schema: Draw the figure described below. Then solve for length PR. Right Triangle PQR with the following characterist

ics: PQ is perpendicular to PR, QR = 47 mm, and Angle Q = 52°
Mathematics
1 answer:
Marina CMI [18]1 year ago
6 0

The given triangle is

To solve for PR, we have to use the sine function which is equivalent to the ratio between the opposite leg and the hypothenuse.

\begin{gathered} \sin 52=\frac{PR}{47} \\ PR=47\cdot\sin 52 \\ PR\approx37.04 \end{gathered}<h2>Hence, PR is 37.04 mm long, approximately.</h2>

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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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