1. Determine whether the following arguments are valid or invalid. If they are v
ID: 3589760 • Letter: 1
Question
1. Determine whether the following arguments are valid or invalid. If they are valid, thern state the rules of inference used to prove validity. If they are invalid, outline precisely (3 marks each) why they are invalid. a. Ifit is snowing then I do not wear shorts to work. I did not wear shorts to work. Therefore, it must be snowing. Everyone taking COMP1501 next semester plays computer games. Therefore, everyone who plays computer games must be taking COMP1501 next b. semester At least one person has been to the moon. Anyone that has been to the moon had to travel through space. Everyone who has travelled through space has experienced microgravity. Therefore, at least one person has experienced microgravity. c. 2. Prove, by indirect proof, that if n is an integer and n3+ 3 is odd, then n is even. Show (5 marks) all your work. -4x3 - 2x2 + 12x 4 is a negative value for every integer (5 marks) 3. Prove or disprove that x in the range -1sx s 3. 4. Prove that (1 x)5 25x1 for all positive integers x. (5 marks)Explanation / Answer
Hi,You have asked multiple questions as part of single question, which is against chegg policy, please post others as separate questions and we will be happy to help you :)
Answering the first one here:
1. This is boolean algebra question, In such questions, first form the predicates and assign truth values for the given statements.
a. the predicates will be
X- it is snowing
Y- I do not wear shorts to work,
now whenever if then is used, it mean implication, so its given in question that X->Y.
now its also given, Y is true,
So, two possibilities X is TRUE or X is FALSE,
if X is true, Y must be true, which is correct
if X is false, Y is TRUE, still the statement X->Y holds, hence we cannot infer this, hence invalid
b. the predicates here are
X- students taking COMP1501 next semester
Y- playing computer games
Now, given for all elements in X, X -> Y i.e if X then Y is true
now, the implication can be true for X is FALSE and Y is TRUE, i.e there can be elements who did not take COMP1501 but do play computer games,
hence the inference is invalid
c.the predicates here are
X-A person has been to moon
Y- A person had to travel through space
Z- experienced micro gravity
Given at least for atleast one person X is true,
also given X->Y, implies there is atleast one person for which Y is true.
also given Y->Z, implies there is atleast one person for which Z is true,
i.e atleast one person has experienced micro gravity
Thumbs up if this was helpful, otherwise let me know in comments
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