Assignment:
Q1. Let p represent a statement having a truth value T, q represent a statement having a truth value F, and r represent a statement having a truth value T. Find the truth value of each of the following: ( a) p Λ ( ~ q)
( b) p Λ q Λ r
( c) p Λ ( q V r)
( d) ~( p Λ q)
( e) (~ p) V (~ q)
Q2. Determine the truth of the following conditionals: ( a) If 5 is larger than 10, then a penny is worth more than $ 1.00. ( b) If 1 foot equals 12 inches, then z is the last letter of the alphabet.
( c) If 60 seconds equal 1 minute, there are 30 hours in a day.
Q3. ( p Λ q) → ( p V q)
Q4. ( p Λ q) ↔ ( p V q)
Q5. p V ( q Λ r) and ( p V q) Λ ( p V r)
Q6. For the statement I will go to a movie, or I will go to a ball game, which of the following is equivalent to its negation? ( a) I will not go to a movie, or I will not go to a ball game. ( b) I will go to a movie, and I will not go to a ball game. ( c) I will not go to a movie, and I will not go to a ball game.
Q7. If U={ a, b, c, d, e, f}, A={ a, b}, and B={ b, c, d}, find ( a) A? ( b) B? ( c) ( A U B) ( d) ( A ∩ B)
Q8. Find A U B where A={ x | x is an even integer greater than 3} B={ x | x is an odd integer greater than 10}
Provide complete and step by step solution for the question and show calculations and use formulas.