Answer to Question #335742 in Discrete Mathematics for seven walou

Question

Let P(x, y) be the statement "x takes y ", where the domain for x consists of all people and y consists of train to work.

a Everyone takes train to work.

b There is someone who took train to work.

c There is someone who took at least one train to work.

d Everyone takes at least one train to work.

e Someone takes at least one train to work.

Answer 1

$a. \forall x \forall y \, P(x,y)$

b.$\exists x \forall y \, P(x,y)$

c. $\exists x \exists y \, P(x,y)$

d. $\forall x \exists y \, P(x,y)$

e. $\exists x \exists y \, P(x,y)$