Let Rx y be the statement x has responded to a post by y whe

Let R(x, y) be the statement \"x has responded to a post by y,\" where the universe of discourse consists of all the students in WBIT 2300 this semester. Translate the statement into English: yxR(x,y) .

There is someone in the class who has had everyone in the class respond to at least one of his or her posts.

There is someone in the class who has responded at least one post of each person in the class.

Everyone in the class has had somebody respond to one of his or her posts.

Solution

The universal quantification of a propositional function P(x) is “P(x) for all values of x in the domain.” Notation: xP(x), where is called the universal quantifier.

The existential quantification of a propositional function P(x) is the proposition “There exists an element x in the domain such that P(x).” Notation: xP(x), where is called the existential quantifier.

SO here in this problem R(x, y) is stated as \"x has responded to a post by y\" where domain is all the students in WBIT 2300 of a particular semester.

yxR(x,y) can be written as

There exists atleast one student y(i.e.,y) in the class whose post has been responded by each and every student x(i.e.,x) in the class.