Suppose each of the following statements is true. Laura is in the seventh grade. Laura got an A on the mathematics test or Sarah
got an A on the mathematics test. If Sarah got an A on the mathematics test, then Laura is not in the seventh grade. If possible, determine the truth value of each of the following statements. Carefully explain your reasoning. (a) Laura got an A on the mathematics test. (b) Sarah got an A on the mathematics test. (c) Either Laura or Sarah did not get an A on the mathematics test
1 answer:
Answer:
a) is TRUE
b) is FALSE
c) is TRUE
Step-by-step explanation:
Let's call the propositions
<em>P: Laura is in the seventh grade </em>
<em>Q: Laura got an A on the mathematics test </em>
<em>R:Sarah got an A on the mathematics test </em>
Then we have that the following propositions are true
P, Q v R (Q or R) and R---> ~P (if R then not P)
By watching at the truth table attached, we can see that the only row that satisfies all that conditions is the second one highlighted.
From there we can deduct that,
a) is TRUE
b) is FALSE
c) is TRUE
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