Convert sentence into First order predicate logic.

Question

a) rabin likes only CSit Course b)science course are hard. c)all courses in CSIT are easy d)CSC 101 is a csit course.

a) Likes(rabin, CSit) $\land$ (Likes(rabin, x) $\implies$ x = CSit). Can you continue? — Adrian Keister, Jun 12 '18 at 17:19
You can do these in multiple ways. b) is probably something like this: TypeOfCourse(x)=Science $\implies$ Hard(x). M.SE is not really a homework site. You need to look at the pattern of these solutions, and do some work yourself. Otherwise, you learn nothing. — Adrian Keister, Jun 12 '18 at 17:26
Well, that syntax makes "course" a predicate. You could work with that like this: (course(x) $\land$ type_of_course(x) = science) $\implies$ hard(x). You have to have a variable in this sort of expression, so you can quantify over it. — Adrian Keister, Jun 12 '18 at 17:31
so we can write for c) (course(x) ∧ type_of_course(x) = csit) ⟹ easy(x) will this be correct ? or (course(x) ∧ csit(x) ⟹ easy(x) — Daily Observations, Jun 12 '18 at 17:34
for d) Vx: csc101(x) -----> CSIT(x,Course) ? will this be correct sir? — Daily Observations, Jun 12 '18 at 17:41
Close. I would just do $\forall x:$ csc101(x) $\implies$ CSit(x). Remember what CSit(x) means: that the predicate CSit is true of x. — Adrian Keister, Jun 12 '18 at 17:45
thank you sir . and the last question *) Everyone's DNA is unique and is derived from their parents DNA ? into predicate logic — Daily Observations, Jun 12 '18 at 17:50

Adrian Keister · Accepted Answer · 2018-06-12T17:59:53.553

1

For completeness, I'll write up the answers in the comments: \begin{align*} &a)\qquad (\forall\,x)[(\text{Likes}(\text{rabin},\text{CSit})\;\land\;\text{Likes}(\text{rabin},x))\implies x=\text{CSit}] \\ &b) \qquad (\forall\,x)[\text{TypeOfCourse}(x)=\text{Science}\implies\text{Hard}(x)] \\ &c)\qquad (\forall\,x)[(\text{Course}(x)\;\land\;\text{TypeOfCourse}(x)=\text{CSit})\implies\text{Easy}(x)] \\ &d)\qquad (\forall\,x)[\text{CSC101}(x)\implies\text{CSit}(x)] \\ &e)\qquad (\forall\,x)(\forall\,y)[(\text{DNA}(x)=\text{DNA}(y)\implies x=y)\;\land\;\text{Parent}(x,y) \implies\text{DNAIsDerivedFrom}(y,x)]. \end{align*}

edited Jun 12 '18 at 17:59

answered Jun 12 '18 at 17:52

Adrian Keister

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thank you sir . and the last question *) Everyone's DNA is unique and is derived from their parents DNA ? into predicate logic? – Daily Observations Jun 12 '18 at 17:52
That's tricky. You can see my solution. – Adrian Keister Jun 12 '18 at 18:00
so basically we are assuming DNA of x and y is equal in first line.. how about this (∀x)(∀y):[ (child(x), parents(y) ) ∧ DNA=x=y -----> DNAIsDerivedFrom(x,y)] – Daily Observations Jun 12 '18 at 18:12

Convert sentence into First order predicate logic.

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