How many students are enrolled in a course either in calculus, discrete mathematics, data structures, 7. or programming languages at a school if there are 507, 292, 312, and 344 students in these courses, respectively; 14 in both calculus and data structures; 213 in both calculus and programming languages; 211 in both discrete mathematics 558 and data structures; 43 in both discrete mathematics and programming languages; and no student may take calculus and discrete mathematics, or data structures and programming languages, concurrently

974

Step-by-step explanation:

Let assume that:

The set of student that took part in Calculus be = C

Those that took part in discrete mathematics be = D

Let those that took part in data structures be = DS; &

Those that took part in Programming language be = P

Thus;

{C} = 507

{D} = 292

{DS} = 312

{P} = 344

For intersections:

{C ∩ DS} = 14

{C ∩ P} = 213

{D ∩ DS} = 211

{D ∩ P}  =43

{C ∩ D} = 0

{DS ∩ P} = 0

{C ∩ D ∩ DS ∩ P} = 0

According to principle of inclusion-exclusion;

{C ∪ D ∪ DS ∪ P} = {C} + {D} + {DS} + {P} - {C ∩ D} - {C ∩ DS} - {C ∩ P} - {D ∩ DS} - {D ∩ P} - {DS ∩ P}

{C ∪ D ∪ DS ∪ P} = 507 + 292 + 312 + 344 - 14 - 213 - 211 - 43 - 0

{C ∪ D ∪ DS ∪ P} = 974

Hence, the no of students that took part in either course = 974

19.side- angle- side

20. angle- side- angle

step-by-step explanation: