1. (a) Use truth tables to prove that an implication is always equivalent to its contrapositive. Give an example, in English, where this is so.
(b) Use truth tables to prove that an implication may not be equivalent to its converse. Give an example, in English, where this is so.
2. Determine whether each of the following are true. Don't forget to explain.
(a) If 2+2=5then1+1=2
(b) If 2 + 3 =5then 1 + 1 = 3
(c) The converse of part (a)
3. Prove the following:
Let a and b be any integers. If n is an odd integer the n^2 is an odd integer.
4. Consider the statement; "If a
(a) Write the converse of this statement. Is the converse true. Explain.
(b) Write the contrapositive of this statement (be careful, check table 6, De Morgan law for the negation of an "and" statement.) Is the contrapositive true? Explain.
5. How many bit strings of length 8 are palindromes? Note a palindrome is a "string" of letters or numbers which read the same "frontwards" and " backwards". Examples: MOM, 1101011, 10111101 are palindromes.