What is the probability of the complement of rolling a number less than 5 by using a six sided dye

Mathematics

1 answer:

IrinaVladis [17]3 years ago

3 0

Answer:

2/3

Step-by-step explanation:

Less than 5 is 1,2,3,4 and 4 out of 6 is also equal to 2/3

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Select all that apply.

nekit [7.7K]

Answer:

The individuals are observed the exact way they act in real life.

Step-by-step explanation:

There are two main types of studies in research; one is controlled or experimental and the other is observational.

In observational studies, the individuals participating in study are not manipulated or intervened or controlled in any way by the researcher.

Hence the statements best describes a characteristic of an observational study is the individuals are observed the exact way they act in real life !

4 0

3 years ago

Suppose you want to prove a theorem of the form p → (q ∨ r). Prove that this is equivalent to showing that (p ∧ ¬q) → r.

tino4ka555 [31]

You "distributed" the negation inside the parenthesis. Let's focus on the $\lnot (p\wedge \lnot q)$ part.

We can distribute the negation inside the parenthesis by negating every term, and switching and with or, and vice versa. So, you have

$\lnot (p\wedge \lnot q) \equiv (\lnot p) (\lnot \wedge) (\lnot \lnot q)$

Of course, writing $\lnot \wedge$ is improper, I was just stressing the fact that we distributed the negation to every term in the parenthesis. So, since a double negation cancels out, you're left with

$\lnot (p\wedge \lnot q) \equiv \lnot p \lor q$

which of course implies that

$\lnot (p\wedge \lnot q) \lor q \equiv (\lnot p \lor q) \lor q$

Edit: I actually derived the expression in the opposite order, but since they are equivalent, it doesn't really matters where you start from and where you get to. Anyway, if you actually want to derive $\lnot (p \wedge \lnot q) \lor r$ from $(\lnot p \lor q)$ , you simply have to negate the first parenthesis and distribute the negation as discussed.