The diagram represents three statements: p, q, and r. for what value is both p ∧ r true and q false?
2
4
5
9

9

Step-by-step explanation:

From the diagram:

So, correct option is 9 cases.

The correct option is 4. For value 9 both p ∧ r true and q false.

Step-by-step explanation:

The diagram represents three statements: p, q, and r.

We need to find the value for which p ∧ r is true and q false.

p ∧ r true mean the intersection of statement p and r. It other words p ∧ r true means p is true and r is also true.

From the given venn diagram it is clear that the intersection of p and r is

p ∧ r true and q false means intersection of p and r but q is not included.

From the given figure it is clear that for value 2 all three statements are true. So, the value for which both p ∧ r true and q false is

Therefore the correct option is 4.

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.