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 F F T F
T F F T T T T T
F T T F T T T T
F F T T F T F F
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).
15 = 5 x 3 = 5 x √3 x √<span>3
so
15 / (5</span><span> √</span>3)
= (5 x √3 x √3)/ (5 x √3) ............( 5 x √3 are canceled out)
= √3
or
= 1.73
Given that t<span>he expression
represents the total length across the front of the mansion. Let the length of side I be a, then
</span>
Answer:
Below in bold.
Step-by-step explanation:
1) as ABCD is a rhombuc AC bisects < BAD and < BCD .
Therefore < CAD = 1/2 * 104 = 52 degrees.
2) < ACG = < ADC + < CAD ( External angle of triangle theorem)
Therfore < ACG = 76 + 52 = 128 degrees.
Assume Alan's brother has x coins before Alan gave him 48 coins
x+48=1.4x (increased by 40%)
0.4x=48
x=120
120+140=260
answer is 260 coins
