The statement $\lnot(p\lor\lnot q)\lor(\lnot p \land \lnot q)$ is equivalent to $\lnot p$ , $\lnot(p\lor\lnot q)\lor(\lnot p \land \lnot q) \equiv \lnot p$

Step-by-step explanation:

We need to prove that the following statement $\lnot(p\lor\lnot q)\lor(\lnot p \land \lnot q)$ is equivalent to $\lnot p$ with the use of Theorem 2.1.1.

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

$\equiv (\lnot p \land \lnot(\lnot q))\lor(\lnot p \land \lnot q)$ by De Morgan's law.

$\equiv (\lnot p \land q)\lor(\lnot p \land \lnot q)$ by the Double negative law

$\equiv \lnot p \land (q \lor \lnot q)$ by the Distributive law

$\equiv \lnot p \land t$ by the Negation law

$\equiv \lnot p$ by Universal bound law

Therefore $\lnot(p\lor\lnot q)\lor(\lnot p \land \lnot q) \equiv \lnot p$

4 0

3 years ago

What is the common ratio of the sequence -360, 120, -40, 13.33,...?

iogann1982 [59]

-360 * -1/3=120
120 * -1/3=-40
the numbers are being multiplied with with -1/3 so cr= -1/2

-1/3

Mark brainliest please

3 0

3 years ago

What is the equation of the line in slope intercept form from the graph.

defon

Answer:

y=4/3x-2

Step-by-step explanation:

We know the base equation is mx+b and the y-intercept is at -2 so we can determine that as the b value. The m value is 4/3 because if you look at where the line meets the next point is over 3 and up 4 indicating that the m value is 4/3. Hope this helps!

7 0

3 years ago

Read 2 more answers

Calculate the slope of the points (2,1) and (3,4). show all your work.

Angelina_Jolie [31]

Answer:

The slope of this line would be 3.

Step-by-step explanation:

To find the slope of any line, use the slope formula and the points given.

m(slope) = (y2 - y1)/(x2 - x1)

m = (4 - 1)/(3 - 2)

m = 3/1

m = 3

3 0

3 years ago