Example solution based on the novel ''Jane Eyre''

Task 5: Variables

1. Provide a variable assignment function g which maps the variables x₁, ..., x₁₀ to members of your universe.

2. Provide one formula that contains two occurrences of variables.

3. Compute the truth value of this formula with respect to your assingment function g.

1. Variable assignment function

• g(x₁) = JaneEyre
• g(x₂) = JaneEyre
• g(x₃) = MrRochester
• g(x₄) = MrRochester
• g(x₅) = BerthaMason
• g(x₆) = St.John
• g(x₇) = BerthaMason
• g(x₈) = MrRochester
• g(x₉) = JaneEyre
• g(x₁₀) = JaneEyre

2. One formulae with two occurrences of variables

Formula: family-of(st.john,x₉) ∧ female(x₇)

3. Interpretation of the formula

Given the model from the earlier tasks and the variable assignment function g, we can compute the truth of the formula as follows:

[[family-of(st.john,x₉) ∧ female(x₇)]]^g = 1
iff [[family-of(st.john,x₉)]]^g = 1 and [[female(x₇)]]^g = 1
iff < I(st.john),g(x₉) > ∈ I(family-of) and < g(x₇) > ∈ I(female)
iff < St.John,JaneEyre > ∈ I(family-of) and < BerthaMason > ∈ I(female)

Since both conditions are met, the formula is true.

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Back to the assignment sheet of Chapter 2.