Karachi earns $5 for each umbrella that he
1 answer:
The equation to represent the number of umbrellas (u) and ponchos (p) he sold last week is 5u + 3.5p = 190
<em><u>Solution:</u></em>
Given that Karachi earns $5 for each umbrella that he sells and $3.50 for each rain poncho that he sells
Thus we can say,
Amount earned from 1 umbrella = $ 5
Amount earned from 1 rain poncho = $ 3.50
To find: equation to represent the number of umbrellas (u) and ponchos (p) he sold last week.
Let "u" be the number of umbrellas sold
Let "p" be the number of ponchos sold
He earned $190 last week selling ponchos and umbrellas
<em><u>Thus we can frame a equation as,</u></em>
number of umbrellas sold x Amount earned from 1 umbrella + number of ponchos sold x Amount earned from 1 rain poncho = $ 190
Thus the equation to represent the number of umbrellas (u) and ponchos (p) he sold last week is found
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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.
