Use Euler diagrams to determine whether the argument is valid

Which statement is correct ? (a){1}∈{1,2,3} (b){1}∉{1,2,3} (c){1}⊆{1,2,3} (d){1}⊂{1,2,3}

Determine if the conclusion follows logically from the premises.  You must submit proof either with an Euler diagram, a TT, or state a standard form of argument as it applies to the premises. Premise: No passive individuals are folks who live well.Premise: All self-actualized persons are folks who live well.Conclusion: No self-actualized persons are passive individuals. Valid argument Invalid argument

1. Let R+ := {x € R|x > 0}. Write negations for the following statements and determine if the original statement or its negation is true. a) 3x € + Vy € R+ (xy < y). b) Vx € R+ y ≤ R+ (xy < y).

Prove the logical statements are equivalent by converting left side to the right hand side (be sure to state equivalence use in conversion like Demorgan, Associativity and Distributive)

EXERCISE 1.11.1: Valid and invalid arguments expressed in logical notation. Indicate whether the argument is valid or invalid. For valid arguments, prove that the argument is valid using a truth table. For invalid arguments, give truth values for the variables showing that the argument is not valid. (h) (1) q→p -q Ap -(p→q) 9 p -q -(p→q) Р q→P q→P P :-(p→q)