6.042/18.] Mathematics for Computer Science February 2, 2005 Srini devadas and Eric Lehman Notes for Recitation 1 logIc A proposition is a statement that is either true or false. Propositions can be joined by and","or","not"," implies", or"if and only if". For each of these connective, the defini- tion and notational shorthand are given in the table below. here a and b denote arbitrary repositions A and B A or B not A A implies B A if and only if B ABA∧BAVB-A A→B 今 T FIF TTF F F T F F FF F a predicate is a proposition whose truth depends on the value of one or more variables If P is a predicate then vx∈SP(x means that the predicate is true for every value of r in the set s. similarly x∈SP(x means that the predicate is true for at least one value of r in the set s.6.042/18.062J Mathematics for Computer Science February 2, 2005 Srini Devadas and Eric Lehman Notes for Recitation 1 1 Logic A proposition is a statement that is either true or false. Propositions can be joined by “and”, “or”, “not”, “implies”, or “if and only if”. For each of these connective, the defini￾tion and notational shorthand are given in the table below. Here A and B denote arbitrary propositions. A and B A or B not A A implies B A if and only if B A B T T A ∧ B A ∨ B ¬A A ⇒ B A ⇔ B T T F T T T F F T F F F F T F T T T F F F F F T T T A predicate is a proposition whose truth depends on the value of one or more variables. If P is a predicate, then ∀x ∈ S P(x) means that the predicate is true for every value of x in the set S. Similarly, ∃x ∈ S P(x) means that the predicate is true for at least one value of x in the set S