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Select the option, which is the logical equivalent of the statement given below:If I like the music then I will give you a prize.1. If I do not give you a prize then I have not liked the music.2. If I give you a prize then I have liked the music.3. If the music is sweet then I will like it.4. I always give prize after listening good music. |
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Answer» Correct Answer - Option 1 : If I do not give you a prize then I have not liked the music. Concepts: If 'p' then 'q' , denoted by p → q where p and q are the hypothesis and conclusion respectively. p → q denotes implies also, ~ p denotes not p means negation ~ q denotes not q means negation q → p denotes converse, which means if q then p. the converse is not true even if the implication is true. ~ p → ~ q denotes inverse, which means if not p then not q. the inverse is not true even if the implication is true. ~ q → ~ p contrapositive, the contrapositive is true if the implication is true and vice versa. Given: p : I like the music q : I give you a prize Truth table
Where T is true denotes positive statement and F is False denotes the negative statement, The logical equivalence from the truth table : Implication and contrapositive result is the same i.e, if p happens then q will happen which implies if q won't happen then p also won't happen. Thus "If I like the music then I will give you a prize" logical equivalent statement is "If I do not give you a prize then I have not liked the music". Hence, option 1 is the correct answer. NOTE: This is not an english language problem, It is about discrete mathematics proposition logic equivalence. |
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