Question

Q1. Formulate the logical constraints for the following statements (where A, B, C, and D are all binary variables):

a. If A happens then B or C happens.

b. If A and B happen then C and D must happen.

c. If A happens or B does not happen then C or D must happen.

d. If A happens or B happens then C and D happen.

This has previously been posted before on Chegg but there are conflicting answers and comments to the questions/responses.

Answer 1

NOTE: All the assumed events of A, B, C, D can only have two values: true or false and hence they are binary variables.

Ans a.

A = event where value of variable 'temp' is even

B = event when 'temp' is divisible by 6.

C = event when 'temp' is divisible by 3.

if ( temp % 2 == 0 )

{

int a = temp/6; // B has occurred here then only the logic reaches this point!

}

else if ( temp % 3 == 0 )

{

int a = temp/6; // C has occurred here then only the logic reaches this point!

}

Ans b.

A = 'temp' is divisible by 2

B = 'temp' is divisible by 3

C = 'temp' is divisible by 6

D = 'temp' is divisible by multiples of 6

if (( temp % 2 == 0 ) && ( temp % 3 == 0 ))

{

int a = temp/6; // a is integer and whole number since C has occured.

int b = temp/12; // Here, 12 is a multiple of 6. Also, b is integer and while number since D has occured.

}

Ans c.

A = 'temp' is divisible by 2

B = 'temp' is divisible by 3

C = 'temp' is divisible by 7

D = 'temp' is divisible by multiples of 6

if (( temp % 2 == 0 ) || ( temp % 3 == 0 )) //only the conditional operator is changed.

{

int a = temp/7; // a is integer and whole number since C has occurred but this is false!

int b = temp/12; // Here, 12 is a multiple of 6. Also, b is integer and while number since D has occured.

}

Ans d.

A = 'temp' is divisible by 2

B = 'temp' is divisible by 3

C = 'temp' is divisible by 6

D = 'temp' is divisible by multiples of 6

if (( temp % 2 == 0 ) || ( temp % 3 == 0 )) //only the conditional operator is changed.

{

int a = temp/6; // a is integer and whole number since C has occurred.

int b = temp/12; // Here, 12 is a multiple of 6. Also, b is integer and while number since D has occured.

}

Please comment for doubts!