Homework Set1 Solutions

• exposé

Math 326 Fall 2010 Homework Set 1 Solutions 2.1-4 Let Q(n) be the predicate “n2 ≤ 30.” (a) Write Q(2), Q(−2), Q(7), and Q(−7) and indicate which of these statements are true and which are false. Q(2) ⇐⇒ 22 ≤ 30 ⇐⇒ 4 ≤ 30 ⇐⇒ T Q(−2) ⇐⇒ (−2)2 ≤ 30 ⇐⇒ 4 ≤ 30 ⇐⇒ T Q(7) ⇐⇒ 72 ≤ 30 ⇐⇒ 49 ≤ 30 ⇐⇒ F Q(−2) ⇐⇒ (−7)2 ≤ 30 ⇐⇒ 49 ≤ 30

• -6 use
• valid argument with true premises
• universal modus
• converse error
• -13 state
• valid application of universal modus ponens
• valid conclusions
• proof
• statement