kwizNET Subscribers, please login to turn off the Ads!
Email us to get an instant 20% discount on highly effective K-12 Math & English kwizNET Programs!

Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

High School Mathematics - 2
14.4 Tautologies

A statement that is always true for all logical possibilities is called a tautology.
A statement that is always false is called a contradiction.
Thus the truth table of a tautology will have T and only T in the last column while a contradiction will have F and only F in the last column. Hence to determine whether a given statement is tautology or not, we construct the truth table and see whether the last column contains all T's or not.
All tautologies are true by virtue of their logical structure, and their tuth is independent of anything to which the sentences might refer. In other words, a tautology is logically true, and its truth has nothing to do with whatever the sentence may be talking about.

Example: Prove that the sentence ' It is wet or it is not wet' is a tautology.
Solution: The sentence may be symbolised by p v ~p where p symbolises the sentence 'It is wet '. The truth table is as shown below.
p ~qp v ~q
TFT
FTT



Q 1:
Answer:

Q 2: Use truth table to establish which of the following statements is tautology or contradiction. [(~p) v q] v [p ^ (~q)]
Contradiction
Tautology

Q 3: Use truth table to establish which of the following statements is tautology or contradiction. (p v q) v (~p)
Tautology
Contradiction

Q 4: Use truth table to establish which of the following statements is tautology or contradiction. [(~q) ^ p] ^ q
Contradiction
Tautology

Q 5: Use truth table to establish which of the following statements is tautology or contradiction. ~[p ^ (~p)]
Tautology
Contradiction

Q 6: Show by means of a truth table that the statement p v ~p is a tautology and the statement p ^ ~p is a contradiction.
Answer:

Q 7: Use truth table to establish which of the following statements is tautology or contradiction. ~[p v (~p)]
Contradiction
Tautology

Q 8: Use truth table to establish which of the following statements is tautology or contradiction. p v ~(p ^ q)
Contradiction
Tautology

Question 9: This question is available to subscribers only!

Question 10: This question is available to subscribers only!


Subscription to kwizNET Learning System offers the following benefits:

  • Unrestricted access to grade appropriate lessons, quizzes, & printable worksheets
  • Instant scoring of online quizzes
  • Progress tracking and award certificates to keep your student motivated
  • Unlimited practice with auto-generated 'WIZ MATH' quizzes
  • Child-friendly website with no advertisements
  • Choice of Math, English, Science, & Social Studies Curriculums
  • Excellent value for K-12 and ACT, SAT, & TOEFL Test Preparation
  • Get discount offers by sending an email to discounts@kwiznet.com

Quiz Timer