400 college students were asked whether they liked Gorkhapatra or Kantipur or Samacharpatra. It was found that 140 likd Gorkhapatra, 165 liked Samacharpatra and 165 liked Kantipur. Moreover, 60 likd Gorkhapatra only, 70 liked Samacharpatra only, 80 liked Kantipur only, 50 liked all three newspaper. Using necessary set notations and Venn-diagram, calculate the number of students who liked exactly two of these three newspapers and who dislike any one of these three newspapers.

Given: ad¯¯¯¯¯ is an altitude. prove: ab2+ac2=cb2 right triangle a b c with right angle a. point d lies on side b c and segment a d is drawn. angle a d c is a right angle. drag and drop a reason into each box to correctly complete the two-column proof. statement reason ad¯¯¯¯¯ is an altitude, and ∠bac is a right angle. given ∠adb and ∠adc are right angles. definition of altitude ∠bac≅∠bda ? ∠bac≅∠adc ? ∠b≅∠b ? ∠c≅∠c reflexive property of congruence △abc∼△dba ? △abc∼△dac aa similarity postulate abbd=cbab ? ab2=(cb)(bd) cross multiply and simplify. acdc=cbac polygon similarity postulate ac2=(cb)(dc) cross multiply and simplify. ab2+ac2=ab2+(cb)(dc) addition property of equality ab2+ac2=(cb)(bd)+(cb)(dc) substitution property of equality ab2+ac2=(cb)(bd+dc) ? bd+dc=cb segment addition postulate ab2+ac2=cb2 substitution property of equality