Daisy is a botanist who works for a garden that many tourists visit. The function f(s) = 3s + 35 represents the number of flowers that bloomed, where s is the number of seeds she planted. The function s(w) = 15w represents the number of seeds she plants per week, where w represents the number of weeks. Part A: Write a composite function that represents how many flowers Daisy can expect to bloom over a certain number of weeks. (4 points)

Part B: What are the units of measurement for the composite function in Part A? (2 points)

Part C: Evaluate the composite function in Part A for 36 weeks. (4 points)
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amaya171

19.12.2021

Mathematics

The statement $((p \lor q) \land (p \implies r) \land (\neg r)) \implies q$ is a tautology.

Step-by-step explanation:

A truth table shows how the truth or falsity of a compound statement depends on the truth or falsity of the simple statements from which it's constructed.

We can see from the truth table that the last column contains only true values. Therefore, the statement is a tautology.

Logical equivalences are a type of relationship between two statements or sentences in propositional logic. To simplify an equivalency, start with one side of the equation and attempt to replace sections of it with equivalent expressions. Continue doing this until you have achieved the desired statement form.

$((p \lor q) \land (p \implies r) \land (\neg r)) \implies q \\\equiv \neg[(p \lor q) \land (p \implies r) \land (\neg r)] \lor q$ by implication law

$\equiv \neg[(p \lor q) \land (\neg p \lor r) \land (\neg r))] \lor q$ by implication law

$\equiv \neg(p \lor q) \lor \neg (\neg p \lor r) \lor \neg(\neg r) \lor q$ by de Morgan’s law

$\equiv \neg(p \lor q) \lor \neg (\neg p \lor r) \lor r \lor q$ by Double Negative

$\equiv [(\neg p \land \neg q) \lor (p \land \neg r)] \lor r \lor q$ by de Morgan’s law

$\equiv [(\neg p \land \neg q) \lor q] \lor [(p \land \neg r) \lor r]$ by commutative and associative laws

$\equiv [(\neg p \lor q) \land (\neg q \lor q)] \lor [(p \lor r) \land (\neg r \lor r)]$ by distributive laws

$\equiv (\neg p \lor q) \lor (p \lor r)$ by negation and identity laws

$\equiv (\neg p \lor p) \lor (q \lor r)$ by communicative and associative laws

$\equiv T$ by negation and domination laws

Therefore, the statement is a tautology.

Use a truth table to determine whether the following statement is a contradiction, a tautology or ne

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