A. Determine the truth value of each proposition. 1. ~(pv-q) 2. ~(~p^q) 3.~(pq) 4.~(~p-q) 5.~(p+q) 6.1p1~q...

 

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A. Determine the truth value of each proposition. 1. ~(pv-q) 2. ~(~p^q) 3.~(pq) 4.~(~p-q) 5.~(p+q) 6.1p1~q 7. p-p 8. pA-p 9. pv-p 10. (p^q)~(gp) B. Express each proposition in symbolic form, and find its truth value. 11. If 2+25=27, then 9+12=21. 12. It is not true that September 2 is a Monday if and only if December 25 is a Friday. 13. Jolo is in Batanes or Basco is in Sulu. 14. It is not true that a ray has a fixed length or segment has endpoints. C. Write the converse, inverse, and contrapositive of the following statement: 15. If two diagonals of a quadrilateral are congruent, then the quadrilateral is a rectangle. 16. If two sides of a triangle are congruent, then the corresponding opposite sides are congruent. 17. If a quadrilateral is a parallelogram, then its diagonals bisect each other. 18. If a triangle is right, then it is not equilateral. 19. If two triangles are congruent, then they are similar. D. Determine whether each proposition is a tautology. 20. [(p-q) Ap]-q 21. [(pVq) A-p]-9 22. (p^q)-p 23. [(p) A (a)] (p^q) E. Simplify the following statement: 24. [(pA-q)v (pAr)]v[(~p^~q)v (~p^r)] A. Determine the truth value of each proposition. 1. ~(pv-q) 2. ~(~p^q) 3.~(pq) 4.~(~p-q) 5.~(p+q) 6.1p1~q 7. p-p 8. pA-p 9. pv-p 10. (p^q)~(gp) B. Express each proposition in symbolic form, and find its truth value. 11. If 2+25=27, then 9+12=21. 12. It is not true that September 2 is a Monday if and only if December 25 is a Friday. 13. Jolo is in Batanes or Basco is in Sulu. 14. It is not true that a ray has a fixed length or segment has endpoints. C. Write the converse, inverse, and contrapositive of the following statement: 15. If two diagonals of a quadrilateral are congruent, then the quadrilateral is a rectangle. 16. If two sides of a triangle are congruent, then the corresponding opposite sides are congruent. 17. If a quadrilateral is a parallelogram, then its diagonals bisect each other. 18. If a triangle is right, then it is not equilateral. 19. If two triangles are congruent, then they are similar. D. Determine whether each proposition is a tautology. 20. [(p-q) Ap]-q 21. [(pVq) A-p]-9 22. (p^q)-p 23. [(p) A (a)] (p^q) E. Simplify the following statement: 24. [(pA-q)v (pAr)]v[(~p^~q)v (~p^r)]