1)Give a Boolean Formula on five variables that has exactly one satisfying assig
ID: 3623083 • Letter: 1
Question
1)Give a Boolean Formula on five variables that has exactly one satisfying assignment. Give the satisfying assignment.
2) A couple is a DINK (double income, no kids) if they are married, both work, and
they do not have children. On Jan 1, 2010 Alice and Bob are a DINK. On Jan 1, 2011 Alice
and Bob are NOT a DINK.
• Let M be the statement Alice and Bob are married.
• Let K be the statement Alice and Bob have kids.
• Let A be the statement Alice has a job.
• Let B be the statement Bob has a job.
(a) Give a Boolean formula (a formula with AND, OR and NOT) on the variables M,K,A,B
that is TRUE on Jan 1, 2010 and conveys as much information as possible.
(b) Give a Boolean formula (a formula with AND, OR and NOT) on the variables M,K,A,B
that is TRUE on Jan 1, 2011 and conveys as much information as possible
Explanation / Answer
Well If I understand correctly you can find the answer from number two for number one, because I believe you just have to made up a scenario similar as the one they are giving you but with 5 variables and make it to be true. As for question number two I have this solution in my point of view: on 2010 they are a DINK so, boolean M,K,A,B=true; a) If M && !K && A && B then is TRUE b) if M && K && A && B || M && !K && !A && B then is TRUE some more possible ors (||) in the second one but this is what I came up with. Hope it helps, good luck.
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