Identify if Valid or Invalid argument P -P→-Q -P^ -R .. -PVR O Valid Argument O Invalid Argument ONeither valid nor invalid

Which statement must also be true with a conditional for the statement to be considered a bi-conditional? converse identity contrapositive inverse

Construct a truth table for each of the following statements. (b ^ d) ^ (b v d) ~ (e) (b) (p^r) V (q^r)

Let S(x,y) be the predicate "person x has spoken to person y," where the domain for the variables x and y is the set of all people. Express the following symbolic proposition as an English sentence: xVy(x, y) Every person has spoken to everyone. Some person has spoken to someone. Some person has spoken to everyone. Every person has spoken to someone.

Let P(a, b) and Q(a, b) be the open sentences defined by P(a, b) : a = b andQ(a, b) : a^2 − b^2 = 0, respectively, where the variables a and b can take any value in Z. Determine the truth value of the open sentence Q(a, b) ⇒ P(a, b) for each (a, b) ∈ {(2, −2),(5, 7),(3, 3)}. Explain your answers.  (Z is the set of intergers)

Please help

Let M(x,y) be the predicate "person x has seen movie y," where the domain for x is the set of all people and the domain for y is the set of all movies. Express the following English sentence as a symbolic proposition: "There is a movie that has not been seen by any people." x-M(x,y) ⒸyVx-M(x, y) x-M(x,y) yx M(x,y) -

In first-order logic, an interpretation consists of the following: (Multiple Choice) A. Constants and variables B. Predicates and functions C. Constants, variables, predicates, and functions D. Only variables