Question 8 (2 points)
2 answers:
Answer:
1) Kyle will be able to fill 2 mugs.
2) Cost of 8 gallons of gasoline is $30.40.
3) Fraction of craft completed in 1 hour :
Step-by-step explanation:
1) Amount of hot chocolate made by Kylie =
Amount of hot chocolate in a 1 mug =
Then of hot chocolate will fill be x
x = 2
2)Cost of 12.5 gallons of gasoline =$47.50
Cost of 1 gallons of gasoline =
Cost of 8 gallons of gasoline =
3) Time taken by a Katie to complete craft project =
Fraction of craft completed in
Fraction of craft completed in 1 hour :
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Step-by-step explanation:
To show that a statement is a tautology using truth table - is to show that all the entries in the expression are truths T.
We can do this by taking each statement, expression by expression. For example, to show that
[~p ∧ (p ∨ q)] → q
is a tautology, knowing we have 3 columns, we have 2^3 = 8 rows. We start by putting putting truth values for p, q, and r respectively
Next, we find ~p, then find (p ∨ q), then find ~p ∧ (p ∨ q), before finally arriving at the required [~p ∧ (p ∨ q)] → q
TERMINOLOGIES AND SYMBOLS
- T means Truth
- F means False
- ~p means negation of p.
~p is F if p is T, and vice versa
- ∧ means conjunction.
p ∧ q is T only if p is T and q is T.
- ∨ means disjunction.
p ∨ q is T if either p or q is T.
- → is for conditional 'if then'
p → q is T if both p and q are T, or both p and q are F, or p is F and q is T, otherwise, it is F.
THE STEP BY STEP WORKINGS FOR THE STATEMENTS GIVEN ARE IN THE ATTACHMENT.
