Please help me on this question

The filled out table is shown below

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Explanation:

We have three variables p,q, and r. So we'll have 2^3 = 8 different rows as this table indicates. The 8 rows is to ensure that we handle all possible T/F values for the three variables.

This is where things could get tricky, but I recommend listing four copies of T in the first column, and then four copies of F right below it. That takes care of column p. For column q, we'll have two copies of TTFF to get 8 values total. Then finally column r will have four copies of T,F repeated. This takes care of all possible combos to help fill out the rest of the table.

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For the column labeled ~p, we'll basically flip everything you see in column p. If something is true, then flip it to false, or vice versa. This is the negation of p. The same will go for the ~r column as well.

For the ~p v q column, we'll do a disjunction between ~p and q. A disjunction is only false when both pieces are false; otherwise it's true. So ~p v q is only false when both ~p and q are together false. The v symbol stands for "or".

The last column is doing a conjunction between the (~p v q) column and the ~r column. A conjunction is only true when both pieces are true; otherwise it's false. It's effectively the reverse of a disjunction. The upside down v symbol stands for "and".

Again the filled out table is shown below. It might help to use a piece of paper to cover up some of the rows if things get too cluttered.

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

30005

yes ok