hw1sol

# hw1sol - CSE 20 Discrete Mathematics Fall 2010 Problem Set...

This preview shows pages 1–2. Sign up to view the full content.

CSE 20: Discrete Mathematics Fall 2010 Problem Set 1 Solutions Instructor: Daniele Micciancio Problem 1 1. ( q r ) → ¬ p 2. ¬ p ( q r ) 3. If you can’t vote, you are under 18 or you are from Mars. 4. p → ¬ ( q r ) (By DeMorgan’s law, this is the same as p ( ¬ q ∧ ¬ r ) ) 5. If you can vote, you are not under 18 and you are not from Mars. Problem 2 1. p ( q r ) ? ⇐⇒ ( p q ) r This is not a valid equivalence, since p ( q r ) is false and ( p q ) r is true when p is false and r is true. (see the ﬁrst truth table) 2. p ( q r ) ? ⇐⇒ ( p q ) ( p r ) This equivalence is valid, since p ( q r ) and ( p q ) ( p r ) have the same value for every row in the table. (see the ﬁrst truth table) 3. ¬ ( p q ) ? ⇐⇒ ( ¬ p ∨ ¬ q ) This is not a valid equivalence. For example, when p is true and q is false, ¬ ( p q ) is false, but ( ¬ p ∨ ¬ q ) is true. (see the second truth table)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

hw1sol - CSE 20 Discrete Mathematics Fall 2010 Problem Set...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online