Question

Write equivalent predicate statements for the following English statement

i) Every teacher loves some painter
ii) Some painter loves some teacher
iii) Every teacher who is also a painter loves Bob

Answer 1

Answer:

Every teacher who is also a painter loves Bob

Answer 2

Answer:

The required answer is shown below:

Step-by-step explanation:

Consider the provided information.

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

Let A is the set of teachers, B is the set of painter and C is bob.

Let define a relation $R: A \rightarrowB$ as aRb if a loves b.

i) Every teacher loves some painter

$\forall a\in A\ \exists\ b\in B\ni aRb$

ii) Some painter loves some teacher

$\exists a\in A\ and\ b\in B\ni aRb$

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:

$\forall c\in A\cap B,\ cRC$