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cricket20 [7]
3 years ago
9

In a conjunction, / is true when both / and / are _____; otherwise, / is _____. A. true . . . true B. true . . . false C. false

. . . true D. false . . . false

Mathematics
2 answers:
Blizzard [7]3 years ago
7 0

Answer:The answer to this question would be OPTION B.In a conjunction, / is true when both / and / are TRUE; otherwise, / is FALSE.

A conjunction refers to a compound statement, developed by combining two statement often through the use of the word 'AND'.  For example, the two statements, 'Roses are Red' (statement p) .... 'Violets are Blue' (statement q), can be combined to form a conjunction that reads 'Roses are Red and Violets are Blue.'  When it comes to conjunctions, it is or equivalent to the intersection of the two sets of statements (p and q → p ∩ q) which therefore means that in order for the conjunction to be true, both statements must be true, otherwise, the conjunction is false.

Attached below is a truth table that seeks to further explain the point (note: ^ represent the conjunction).

elena-14-01-66 [18.8K]3 years ago
6 0
The answer to this question would be OPTION B.In a conjunction, / is true when both / and / are TRUE; otherwise, / is FALSE.

A conjunction refers to a compound statement, developed by combining two statement often through the use of the word 'AND'.  For example, the two statements, 'Roses are Red' (statement p) .... 'Violets are Blue' (statement q), can be combined to form a conjunction that reads 'Roses are Red and Violets are Blue.'  When it comes to conjunctions, it is or equivalent to the intersection of the two sets of statements (p and q → p ∩ q) which therefore means that in order for the conjunction to be true, both statements must be true, otherwise, the conjunction is false.

Attached below is a truth table that seeks to further explain the point (note: ^ represent the conjunction).

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The following equations are given:
jarptica [38.1K]

The solution to the variables using equations 1, 2 and 3 is x = 2, y = -1 and z = 3 and the solutions in part b hold for equation 4

<h3>Solving the variables using equations 1 and 2</h3>

There are three variables in the system

To solve the three variables, there must be at least three equations in the system of equations

Hence, the variables cannot be solved because the number of equations is not enough

<h3>Solving the variables using equations 1, 2 and 3</h3>

We have:

3x + z + y = 8

5y - x = -7

3z + 2x - 2y = 15

Make x the subject in (2)

x = 5y + 7

Substitute x = 5y + 7 in (1) and (3)

3(5y + 7) + z + y = 8

15y + 21 + z + y = 8

16y + z = -13

3z + 2(5y + 7) - 2y = 15

3z + 10y + 14 - 2y = 15

3z + 8y = 1

Multiply 16y + z = -13 by 3

48y + 3z = -39

Subtract 3z + 8y = 1 from 48y + 3z = -39

48y - 8y + 3z - 3z = -39 - 1

40y = -40

Divide by 40

y = -1

Substitute y = -1 in x = 5y + 7

x = 5(-1) + 7

x = 2

Make z the subject in 16y + z = -13

z = -13 - 16y

Substitute y = -1

z = -13 - 16(-1)

z = 3

Hence, the solution to the variables using equations 1, 2 and 3 is x = 2, y = -1 and z = 3

<h3>Can the solution work for equation 4?</h3>

We have:

4x + 5y - 2z = -3

Substitute x = 2, y = -1 and z = 3

4(2) + 5(-1) - 2(3) = -3

Evaluate

-3 = -3 --- this is true

Hence, the solutions in part b hold for equation 4

Read more about system of equations at:

brainly.com/question/12895249

#SPJ1

<u>Missing part of the question</u>

The following equations are given:

Equation #1: 3x + z + y = 8

Equation #2: 5y - x = -7

Equation #3: 3z + 2x - 2y = 15

Equation #4: 4x + 5y - 2z = -3

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