PHP

Negate the following Boolean expressions using both approaches.

i.   $b != 4

ii.  $a * 3 + 2 > 0

iii. !($a == 5 && $b >= 7)

  iv.  $a == true

  v.   $b > 7 && !($x > 4)

  vi.  $a == 4 || $b != 2

Solution

First Approach

i.   !($b != 4)

ii.  !($a * 3 + 2 > 0)

iii. !(!($a == 5 && $b >= 7)), or the equivalent $a == 5 and $b >= 7

Notice: Two negations result in an affirmative. That is, two NOT operators in a row negate each other.

iv.  !($a == true)

v.   !($b > 7 && !($x > 4))

vi.  !($a == 4 || $b != 2)

Second Approach

i.   $b == 4

ii.  $a * 3 + 2 <= 0

Notice: Please note that arithmetic operators are not negated. Don’t you ever dare replace the plus (+) with a minus (-) operator!

iii. !($a != 5 || $b < 7)

Notice: Please note that NOT operator remains intact.

iv.  $a != true

v.   $b <= 7 || !($x <= 4)

vi.  $a != 4 && $b == 2

Java, C++, C#

Negate the following Boolean expressions using both approaches.

i.   b != 4

ii.  a * 3 + 2 > 0

iii. !(a == 5 && b >= 7)

  iv.  a == true

  v.   b > 7 && !(x > 4)

  vi.  a == 4 || b != 2

Solution

First Approach

i.   !(b != 4)

ii.  !(a * 3 + 2 > 0)

iii. !(!(a == 5 && b >= 7)), or the equivalent a == 5 and b >= 7

Notice: Two negations result in an affirmative. That is, two NOT operators in a row negate each other.

iv.  !(a == true)

v.   !(b > 7 && !(x > 4))

vi.  !(a == 4 || b != 2)

Second Approach

i.   b == 4

ii.  a * 3 + 2 <= 0

Notice: Please note that arithmetic operators are not negated. Don’t you ever dare replace the plus (+) with a minus (-) operator!

iii. !(a != 5 || b < 7)

Notice: Please note that NOT operator remains intact.

iv.  a != true

v.   b <= 7 || !(x <= 4)

vi.  a != 4 && b == 2

Visual Basic

Negate the following Boolean expressions using both approaches.

i.   b <> 4

ii.  a * 3 + 2 > 0

iii. Not(a = 5 And b >= 7)

  iv.  a = True

  v.   b > 7 And Not(x > 4)

  vi.  a = 4 Or b <> 2

Solution

First Approach

i.   Not(b <> 4)

ii.  Not(a * 3 + 2 > 0)

iii. Not(Not(a = 5 And b >= 7)), or the equivalent a = 5 And b >= 7

Notice: Two negations result in an affirmative. That is, two NOT operators in a row negate each other.

iv.  Not(a = True)

v.   Not(b > 7 And Not(x > 4))

vi.  Not(a = 4 Or b <> 2)

Second Approach

i.   b = 4

ii.  a * 3 + 2 <= 0

Notice: Please note that arithmetic operators are not negated. Don’t you ever dare replace the plus (+) with a minus (-) operator!

iii. Not(a <> 5 Or b < 7)

Notice: Please note that NOT operator remains intact.

iv.  a != True

v.   b <= 7 Or Not(x <= 4)

vi.  a <> 4 And b = 2

Python

Negate the following Boolean expressions using both approaches.

i.   b != 4

ii.  a * 3 + 2 > 0

iii. not(a == 5 and b >= 7)

  iv.  a == true

  v.   b > 7 and not(x > 4)

  vi.  a == 4 or b != 2

Solution

First Approach

i.   not(b != 4)

ii.  not(a * 3 + 2 > 0)

iii. not(not(a == 5 and b >= 7)), or the equivalent a == 5 and b >= 7

Notice: Two negations result in an affirmative. That is, two NOT operators in a row negate each other.

iv.  not(a == true)

v.   not(b > 7 and not(x > 4))

vi.  not(a == 4 or b != 2)

Second Approach

i.   b == 4

ii.  a * 3 + 2 <= 0

Notice: Please note that arithmetic operators are not negated. Don’t you ever dare replace the plus (+) with a minus (-) operator!

iii. not(a != 5 or b < 7)

Notice: Please note that NOT operator remains intact.

iv.  a != true

v.   b <= 7 or not(x <= 4)

vi.  a != 4 and b == 2

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