Let the following statements be given: p = \"Andy is hungry\" q=\"The refrigerat
ID: 638501 • Letter: L
Question
Let the following statements be given:
p = "Andy is hungry"
q="The refrigerator is empty"
r ="Andy is mad"
(a) Use connectives to translate the following statement into formal logic.
If Andy is hungry and the refrigerator is empty, than Andy is mad.
(b) Construct a truth table for the statement in part (a)
(c) Suppose that the statement given in part(a) is true, and supposed also that Andy is not mad and the refrigerator is empty. Is Andy hungry? Explain how to justify your answer using the truth table.
Explanation / Answer
p = "Andy is hungry"
q="The refrigerator is empty"
r ="Andy is mad"
Ans a:
p ^ q : Andy is hungry and The refrigerator is empty (AND operator)
(p ^ q) => r : If Andy is hungry and the refrigerator is empty, than Andy is mad. (implication operator)
Ans b:
Column No
p
q
r
p^q
(p^q)=>r
1
F
F
F
F
T
2
F
F
T
F
T
3
F
T
F
F
T
4
F
T
T
F
T
5
T
F
F
F
T
6
T
F
T
F
T
7
T
T
F
T
F
8
T
T
T
T
T
T= TRUE, F = FALSE
Ans c:
Given that :
Part(a): (p^q)=>r is TRUE & r=False (Andy is not mad) & q=TRUE (refrigerator is empty).
This Corresponds to the state of Column No 3 in the Truth Table and hence the answer is p = False (Andy is not hungry)
plz comment for any doubt
Column No
p
q
r
p^q
(p^q)=>r
1
F
F
F
F
T
2
F
F
T
F
T
3
F
T
F
F
T
4
F
T
T
F
T
5
T
F
F
F
T
6
T
F
T
F
T
7
T
T
F
T
F
8
T
T
T
T
T
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