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Answer:
Step-by-step explanation:
Let be a set of all students in your class. The set
is the domain. Denote
Consider the statement '<em>A student in your class has a cat, a dog, and a ferret</em>'. 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 '<em>All students in your class have a cat, a dog, or a ferret.' </em>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 '<em>Some student in your class has a cat and a ferret, but not a dog.' </em>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 '<em>No student in your class has a cat, a dog, and a ferret..' </em>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 '<em> For each of the three animals, cats, dogs, and ferrets, there is a student in your class who has this animal as a pet.' </em>
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