Question

can you please answer both question and write clearly

CSC231 Discrete Structures Logical Equivalence This assignment deals with Logical Equivalences. Review section 1.7 of the text before completing the assignment. The assignment may be handed in twice before it is graded. Consider the statements in the left column of the tables below. Translate each into a propositional statement. In the box below, indicate which two statements are logically equivalent. The gray shaded box is the Equation editor that should be used to enter the propositional expression. Question 1 Statement Propositional Statement Whenever there is a puppy in the house, I feel happy if I am happy, then there is a puppy in the house If there is not a puppy in the house, then I am not happy. If I am not happy, then there is no puppy in the house

Answer 1

Let us give notations to make the logic translation easy.

say P for if there is puppy

H for feel happy.

So the condition if there is puppy, I feel happy would be logically represented as P-->H

if I am not happy , there is no puppy would be the contrapositive for the above condition which is logically written as ~H-->~P

Since the contrapositive and the original statement are logically equivalent,

Statement 1: whenever there is puppy, I feel happy and

Statement 4:If I am not happy , there is no puppy

are logically equivalent.

Consider statement 2

If I am happy , then there is puppy translated as H-->P

The contrapositive statement for the above would be

If there is no puppy, then Im not happy represented logically as ~P-->~H which is also the statement 3

Hence Statement 2 and 3 are logically equivalent too.

Moving to Statement 5, lets give the notation S for Im in school today.

and CS for Im in CSC231 class.

The logical translation would be S-->CS

The contrapositive for the above statement would be ~CS-->~S ie If I am not in CSC231 class , then Im not in school today which is also the Statement 7

Hence Statement 5 and 7 are logically equivalent.

Hope this helps

Thank you