Answer to Question #257711 in Discrete Mathematics for kot

Question

Let 𝐴={1,2,3,4}. Determine the truth value of each statement:

i. ∀𝑥 ∈𝐴,𝑥+3<6

ii. ∃𝑥,𝑥+3<6

iii. ∃𝑥,2𝑥2 +𝑥 =15

Answer 1

i.

false: $4+3>6$

ii.

true: $1+3<6$

iii.

false:

$2\cdot1^2+1=3$

$2\cdot2^2+2=10$

$2\cdot3^2+3=21$

$2\cdot4^2+4=36$