Use predicates and quantifiers to express the following statement , "Some students in this class grew up in the same town as at least two other students in this class".

Prove whether the argument is valid or not? All the students who belongs to discrete mathematics class love cricket and football. Some students present here do not love football. Therefore, some students present here do not belong to discrete mathematics class.

Which of the following statements is the contrapositive of the statement, "You win the game if you know the rules but are not overconfident." Select one: a. A necessary condition that you know the rules or you are not overconfident is that you win the game. O b. If you know the rules and are overconfident then you win the game. O c. A sufficient condition that you win the game is that you know the rules or you are not overconfident. O d. If you lose the game then you don't know the rules or you are overconfident. Oe. If you don't know the rules or are overconfident you lose the game.

q6last part plz provide handwritten solution for upvote

write the contrapositive of: “if the earth is red, then the sky is black."

Consider the statement: If tomorrow is a Saturday, then we do not have classes. Write converse, inverse, and contrapositive statements.

5. Rewrite the following proposition as unambiguous English sentences. The relevant predicates are defined as follows: Again, let’s let P be a set of all people a. A(x) means “x is teaching the AI course" b. T(x) means “x is taking AI course" c. F(x) means “x has a twitter account." d. C(x) means “x likes to read." For example, the proposition 3x {P[A(x)^ C(x)]} could be translated as "There is a person who is teaching and likes to read" P [T(x) → (F(x) C(x))] ?

please solve question A and B

Q.6 Convert the following sentence to conjunctive normal form (CNF). (A B) =C (Hint: Study Conjunctive normal form (CNF) and Standard logical equivalences)

A local health clinic often makes this statement to its patients. If you get a flu shot, then you won't get the flu thus winter. (a) Statements p and q are defined as follows. p: You get a flu shot. q: You get the flu this winter. Write the clinic's statement in symbolic form using p and q Symbolic form: __ (b) Suppose the following situation occurred. You got a flu shot. During winter, you got flu. Complete the table to determine the truth of the clinic's statement in this situation. Use T for true and F for false.