Question 1
1.1
∃x (D(x) ∧ M(i, x))
Explanation:
First, we define the predicates and constant symbols:
D(x): This predicate represents the statement "x is a degree," where x is a variable that can take on
different degree values.
M(x, y): This predicate represents the statement "x is a major subject of y," where x and y are
variables that can take on different subject values.
i: This constant symbol represents the subject "Information Systems."
To express the given sentence in predicate logic, we can use the existential quantifier (∃) to
indicate the existence of an object that satisfies the conditions. In this case, we want to express that
there exists a degree with Information Systems as a major subject.
Now, let's break down the translation:
∃x: This part indicates that there exists a degree x.
(D(x) ∧ M(i, x)): Inside the parentheses, we have two conditions joined by the conjunction
operator (∧):
D(x): This condition specifies that x is a degree.
M(i, x): This condition specifies that Information Systems (i) is a major subject of x.
Putting it all together, the translated predicate logic expression ∃x (D(x) ∧ M(i, x)) can be read
as "There exists a degree x such that x is a degree and Information Systems is a major subject of
x."
In summary, the translation represents the existence of a degree where Information Systems is one
of its major subjects.
1.2
∀x (L(x, c) → T(x, c) ∧ M(c, x))
Explanation:
1. "Everyone who loves Computer Science"
2. "takes it as a major subject of a degree"
Let's represent these parts using the given symbols:
1. "Everyone who loves Computer Science": ∀x (L(x, c))
This statement can be read as "For all x, x loves Computer Science."
2. "takes it as a major subject of a degree": ∀x (L(x, c) → T(x, c) ∧ M(c, x))
This statement can be read as "For all x, if x loves Computer Science, then x takes
Computer Science as a major subject of a degree."
1.3
∀x (L(x, c) → ¬H(x, i))
Explanation:
Determine the subject of the sentence: "someone"
1.1
∃x (D(x) ∧ M(i, x))
Explanation:
First, we define the predicates and constant symbols:
D(x): This predicate represents the statement "x is a degree," where x is a variable that can take on
different degree values.
M(x, y): This predicate represents the statement "x is a major subject of y," where x and y are
variables that can take on different subject values.
i: This constant symbol represents the subject "Information Systems."
To express the given sentence in predicate logic, we can use the existential quantifier (∃) to
indicate the existence of an object that satisfies the conditions. In this case, we want to express that
there exists a degree with Information Systems as a major subject.
Now, let's break down the translation:
∃x: This part indicates that there exists a degree x.
(D(x) ∧ M(i, x)): Inside the parentheses, we have two conditions joined by the conjunction
operator (∧):
D(x): This condition specifies that x is a degree.
M(i, x): This condition specifies that Information Systems (i) is a major subject of x.
Putting it all together, the translated predicate logic expression ∃x (D(x) ∧ M(i, x)) can be read
as "There exists a degree x such that x is a degree and Information Systems is a major subject of
x."
In summary, the translation represents the existence of a degree where Information Systems is one
of its major subjects.
1.2
∀x (L(x, c) → T(x, c) ∧ M(c, x))
Explanation:
1. "Everyone who loves Computer Science"
2. "takes it as a major subject of a degree"
Let's represent these parts using the given symbols:
1. "Everyone who loves Computer Science": ∀x (L(x, c))
This statement can be read as "For all x, x loves Computer Science."
2. "takes it as a major subject of a degree": ∀x (L(x, c) → T(x, c) ∧ M(c, x))
This statement can be read as "For all x, if x loves Computer Science, then x takes
Computer Science as a major subject of a degree."
1.3
∀x (L(x, c) → ¬H(x, i))
Explanation:
Determine the subject of the sentence: "someone"
