10–25 years 10 5 20 35
26–40 years 15 10 10 35
41–55 years 20 10 0 30
Total 45 25 30 100
What is the probability (rounded to the nearest whole percent) that a randomly selected person is 10 to 25 years old or prefers drinking rootbeer?
60%
55%
10%
5%
If p is true and ~ q is false, then p -> ~ q is always, sometimes, never false.
If p is true and q is true, then ~ p -> ~ q is always, sometimes, never true.
If p -> q is true and q is true, then p always, sometimes, never is
1. If p is true and q is false, the p -> q is never true.
2. When p is false and q is true, then p or q is always true.
3. If p is true and ~ q is false, then p -> ~ q is never false.
4. If p is true and q is true, then ~ p -> ~ q is always true.
5. If p -> q is true and q is true, then p is always true.
Further Explanation:
The logic gates are used here.
Here, the symbol -> is for implication. Implication p-> q means that if p is true then q must be true.
So let us look at all the questions one by one.
1. If p is true and q is false, the p -> q is always, sometimes, never true.
p -> q
true -> false
The true should imply true so the given statement will never be true.
2. When p is false and q is true, then p or q is always, sometimes, never true.
false or true
We know that in or gate even if one input is true, the whole output is true. So this statement will be always true given p is false and q is true.
3. If p is true and ~ q is false, then p -> ~ q is always, sometimes, never false.
This translates to:
true -> true
So it will never be false.
4. If p is true and q is true, then ~ p -> ~ q is always, sometimes, never true.
This translates to:
false -> false
This will always be true.
5. If p -> q is true and q is true, then p is always, sometimes, never true.
If p->q is true and q is true then p will always be true. "Implies to" states that in p->q, in order for q to be true p has to be true. So p will always be true.
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Answer:
Your answer is: Always true
Step-by-step explanation: