Question

Write equivalent predicate statements for the following English statement
i. Every teacher loves some painter [2]

Answer 1

Answer:

Every teacher is liked by some student"

∀(x)[teacher(x)→∃(y)[student(y)→likes(y,x)]]

∀(x)[teacher(x)→∃(y)[student(y)∧likes(y,x)]]

∃(y)∀(x)[teacher(x)→[student(y)∧likes(y,x)]]

∀(x)[teacher(x)∧∃(y)[student(y)→likes(y,x)]]

My attempt :

"Some student likes x" is ∃(y)[student(y)∧likes(y,x)]

So,

"Every teacher is liked by some student" is

∀(x)[teacher(x)→∃(y)[student(y)∧likes(y,x)]]

Answer 2

Answer:

Consider the provided information.

We need to Write equivalent predicate statements for the following English statement

Step-by-step explanation:

Let define a relation  as aRb if a loves b.

i) Every teacher loves some painter

ii) Some painter loves some teacher

iii) Every teacher who is also a painter loves Bob

Every teacher who is also a painter means A∩B

Therefore, the required predicate statements is: