Let c(x) be the statement "x has a cat," let d(x) be the statement "x has a dog," and let f(x) be the statement "x has a ferret." express each of these statements in terms of c(x), d(x), f(x), quantifiers, and logical connectives. let the domain consist of all students in your class. a) a student in your class has a cat, a dog, and a ferret. b) all students in your class have a cat, a dog, or a ferret. c) some student in your class has a cat and a ferret, but not a dog. d) no student in your class has a cat, a dog, and a ferret. e) for each of the three animals, cats, dogs, and ferrets, there is a student in your class who has this animal as a pet.

Step-by-step explanation:

Let be a set of all students in your class. The set is the domain. Denote

Consider the statement 'A student in your class has a cat, a dog, and a ferret'. This means that so that all three statements C(x), D(x) and F(x) are true. We can express that in terms of C(x), D(x) and F(x) using quantifiers, and logical connectives as follows

Consider the statement 'All students in your class have a cat, a dog, or a ferret.' This means that at least one of the statements C(x), D(x) and F(x) is true. We can express that in terms of C(x), D(x) and F(x) using quantifiers, and logical connectives as follows

Consider the statement 'Some student in your class has a cat and a ferret, but not a dog.' This means that so that the statements C(x), F(x) are true and the negation of the statement D(x) . We can express that in terms of C(x), D(x) and F(x) using quantifiers, and logical connectives as follows

Consider the statement 'No student in your class has a cat, a dog, and a ferret..' This means that none of  the statements C(x), D(x) and F(x) are true. We can express that in terms of C(x), D(x) and F(x) using quantifiers, and logical connectives as a negation of the statement in the part a), as follows

Consider the statement ' For each of the three animals, cats, dogs, and ferrets, there is a student in your class who has this animal as a pet.'

This means that for each of the statements C, F and D there is an element from the domain so that each statement holds true.

We can express that in terms of C(x), D(x) and F(x) using quantifiers, and logical connectives as follows

step-by-step explanation:

here's what happens:

1) the graph of f   = x^2 is shifted 2 units to the right.

2) the resulting graph is reflected in the x-axis, so that the parabola now opens down.

3) this final result is transformed up by 5 units.