1. Use a truth table to test whether the following argument is valid. (Present the truth table, and say whether the argument is valid or invalid. When presenting your truth table you must fill in the truth values in the matrix in the way presented in lecture and in §3.3 of the textbook where it says “Here is a trick for filling in the truth values in the matrix”.) If the argument is invalid, give a counterexample. (¬A → ¬C) ((C ∨ ¬A) ↔ E) ∴ (E∧¬C) 2. Say whether or not the following argument: (¬B ↔ (¬A ∨ ¬¬(A → B))) ¬(A → B) ∴ ¬(¬A∧¬¬B) is an instance of the following argument form: (α ↔ (β ∨ ¬γ)) γ ∴ ¬(β∧¬α) If you say it is an instance, then also say what substitutions of propositions for wff variables have to be made to obtain the argument from the argument form. If you say it is not an instance, explain why.

A truth table is used to:a.Determine the validity of a logical argumentb.Determine the truth value of a compound propositionc.Determine the logical connectives in a propositiond.Determine the inverse of a logical statement

Use symbols to write the logical form of each argument given below, and thenuse a truth table to test the argument for validity.If the positive number is less than 2, then its square is not larger than 4.If square of number is larger than 4, then the number is not less than 2.∴ The positive number is not less than 2 and its square is not larger than 4

Construct a truth table for the formula .

2. Use a tree to test whether the following two propositions are equivalent. (Present the tree, and say whether they’re equivalent or not.) If they’re not equivalent, read off from your tree a model on which the propositions have different truth values (and indicate the path from which you are reading it off). ∀x(Ax → Gx) ∃x(Ax → Gx)

Draw truth-table for negation.