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# Mathematical Logic - Mathematical Logic

11:   Consider two well-formed formulas in propositional logic
F1 : P →˥P F2 : (P →˥P) v ( ˥P →)
Which of the following statement is correct?
 A. F1 is satisfiable, F2 is unsatisfiable B. F1 is unsatisfiable, F2 is satisfiable C. F1 is unsatisfiable, F2 is valid D. F1 & F2 are both satisfiable Answer Report Discuss Option: C Explanation : Click on Discuss to view users comments. Write your comments here:
12:   What can we correctly say about proposition P1:
P1 : (p v ˥q) ^ (q →r) v (r v p)
 A. P1 is tautology B. P1 is satisfiable C. If p is true and q is false and r is false, the P1 is true D. If p as true and q is true and r is false, then P1 is true Answer Report Discuss Option: C Explanation : Click on Discuss to view users comments. Write your comments here:
13:   (P v Q) ^ (P → R )^ (Q →S) is equivalent to
 A. S ^ R B. S → R C. S v R D. All of above Answer Report Discuss Option: C Explanation : Click on Discuss to view users comments. aditya said: (5:02am on Tuesday 1st January 2013) This is not possible.Please check again.If yes then give me solution kriti said: (1:28am on Monday 20th May 2013) make the truth table of the qiestion.then make the truth table of all the options. You will get the answer as (c).Though the calculation is a bit lengthy, but its the only way i found to calculate the answer. NIlesh said: (5:49am on Monday 8th June 2015) question is wrongeach part of and should be true i. e. P->R should be true when (s OR R)is truecase : when P = True and R = True and s = TrueP->R is False but (S OR R) is True. Write your comments here:
14:

The functionally complete set is

 A. { ˥, ^, v } B. {↓, ^ } C. {↑} D. Both (b) and (c) Answer Report Discuss Option: D Explanation : Click on Discuss to view users comments. Write your comments here:
15:   (P v Q) ^ (P→R) ^ (Q → R) is equivalent to
 A. P B. Q C. R D. True = T Answer Report Discuss Option: C Explanation : Click on Discuss to view users comments. Write your comments here: X