Question

Represent the following statements in predicate logic:

i) Every cat is sleeping
ii) Some girl likes David
iii) No one is happy
iv) It is sleeping
v) She likes David
vi) Every student is happy
vii) Some students are happy
viii) No student complained
ix) Not every student complained

Answer 1

The statements can be represented in predicate logic as follows: Every cat is sleeping, Some girl likes David, No one is happy, It is sleeping, She likes David, Every student is happy, Some students are happy, No student complained, Not every student complained.

Step-by-step explanation:

The statements can be represented in predicate logic as follows:

i) Every cat is sleeping

Let C(x) be the statement 'x is a cat'.

Let S(x) be the statement 'x is sleeping'.

The statement can be represented as ∀x (C(x) → S(x)), which reads as 'For every x, if x is a cat, then x is sleeping.'

ii) Some girl likes David

Let G(x) be the statement 'x is a girl'.

Let L(x, y) be the statement 'x likes y'.

The statement can be represented as ∃x (G(x) & L(x, David)), which reads as 'There exists an x, if x is a girl, then x likes David.'

iii) No one is happy

Let H(x) be the statement 'x is happy'.

The statement can be represented as ∀x (~H(x)), which reads as 'For every x, x is not happy.'

iv) It is sleeping

Let S be the statement 'It is sleeping'.

The statement can be represented as S.

v) She likes David

Let L(x, y) be the statement 'x likes y'.

The statement can be represented as L(She, David), which reads as 'She likes David.'

vi) Every student is happy

Let S(x) be the statement 'x is a student'.

Let H(x) be the statement 'x is happy'.

The statement can be represented as ∀x (S(x) → H(x)), which reads as 'For every x, if x is a student, then x is happy.'

vii) Some students are happy

Let S(x) be the statement 'x is a student'.

Let H(x) be the statement 'x is happy'.

The statement can be represented as ∃x (S(x) & H(x)), which reads as 'There exists an x, if x is a student, then x is happy.'

viii) No student complained

Let S(x) be the statement 'x is a student'.

Let C(x) be the statement 'x complained'.

The statement can be represented as ∀x (S(x) → ~C(x)), which reads as 'For every x, if x is a student, then x did not complain.'

ix) Not every student complained

Let S(x) be the statement 'x is a student'.

Let C(x) be the statement 'x complained'.

The statement can be represented as ∃x (S(x) & ~C(x)), which reads as 'There exists an x, if x is a student, then x did not complain.'