4 votes 4 votes Which of the following statements is/are true? $(a\rightarrow b)$ always equals $\bar{a} +b.$ $\bar a+b +a \bar b $ is a tautology. $\left (a\rightarrow b \right).\left(a \bar b \right )$ is satisfiable. III only I and II only II and III only I, II, and III Mathematical Logic tbb-mockgate-2 discrete-mathematics mathematical-logic propositional-logic + – Bikram asked Jan 24, 2017 • edited Sep 12, 2020 by ajaysoni1924 Bikram 324 views answer comment Share Follow See all 4 Comments See all 4 4 Comments reply Tendua commented Jan 24, 2017 reply Follow Share what Is star here ?? 0 votes 0 votes Bikram commented Jan 25, 2017 reply Follow Share * is multiplication 0 votes 0 votes Kabi commented Dec 26, 2017 reply Follow Share C is satisfiable,just put A=false,B=false/true. 0 votes 0 votes akash.dinkar12 commented Jul 29, 2018 reply Follow Share Kabi C is not satisfiable, it is a contradiction when u put A = false, the first term (A→ B) is always true but then(ab') is always false because it is (a∧b'), So entire expression can never be true. I and II only is a true 0 votes 0 votes Please log in or register to add a comment.
1 votes 1 votes 1) a -->b = a' v b = a'+b (Always True) 2) (~a+b) + (a*~b) = a'+b+ab' = a'+ab'+b = a'+b'+b = a'+1 = 1 (Tautology) Here a'+ab' = a'+b' 3) (a-->b)*(a*~b) = (a'+b)*ab' = a'ab'+bab' = 0 (Falsifiable) Hence 1) and 2) are true so correct ans is B. amolagrawal answered Jan 25, 2017 • edited Feb 5, 2017 by amolagrawal amolagrawal comment Share Follow See all 0 reply Please log in or register to add a comment.