Give an example of a valid argument of the form α ∴ ¬α

Determine whether these are valid arguments. a) If x​2​ ​≠ 0, where x is a real number, then x ≠ 0. Let a be a real number with a​2 ​≠ 0; then a ≠ 0.

State the converse, inverse, and contrapositive of the following statement.Then give the truth values of all FOUR statements: Let a, b, c ∈Z+.    If  a | b and a | c then a | ( b + c ) .                         T / F converse­­­­­­­­­­­_______________________________________________________________T / F inverse­­­­­­­­­­­________________________________________________________________ T / F contrapositive_________________________________________________________ T / F

Check if ¬P is a logical consequence of: