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NVIT CSO) 235 Discrete Structures idterm 1 Lectures 1-5 PRINT NAME 1.Verify that

ID: 3585000 • Letter: N

Question

NVIT CSO) 235 Discrete Structures idterm 1 Lectures 1-5 PRINT NAME 1.Verify that the proposition p-(p A ) is a tautology 2, Show that 4p ^-q) ^ ( v q) is a contradiction. * 3. Consider the programming statement . if x > 0 then x- 2x+1 UD -N a. Is this a proposition or a predicate and why? b. Depending on your answer in part a, write it symbolically in proposition or predicate form c What action is taken when x>0, x-0 and xco d. What are the two ways to determine the truth value of a propositionalfu function rage NYIT CSCI 23S Discrete Structures Midterm 1 Lectures 1-5

Explanation / Answer

1. p v ~(p^q)

=p v (~p v ~q)         [De Morgans Law]

=p v ~p v ~q

=(p v ~p) v ~q

This is always true since p V ~p is always true.

2. ( p ^ ~q) ^ (~p v q)

=( p ^ ~q) ^ ~( p ^ ~q)    [De Morgans Law]

If ( p ^ ~q) is a , ~( p ^ ~q) is ~a , this is of the form a ^ ~a which is always false.

Thus, ( p ^ ~q) ^ ~( p ^ ~q) is always false.

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