Question

2. a) Consider the propositions ‘2+3 = 5’ and ’The Sun rises in the West’.

i) Write the disjunction of the statements and give its truth value.

ii) Write the conjunction of the statements and give its truth value.

iii) Write the exclusive disjunction of the statements and give its truth value.

Answer 1

i) Let A= ‘2+3 = 5’ and B=’The Sun rises in the West’. Then the disjunction of the statements

is $A \vee B$ . Since$A = true$ and $B = false$ then $A \vee B=true \vee false=true$

Answer: true

ii) The conjunction of the statements is $A \wedge B$ . Since$A = true$ and $B = false$ then $A \wedge B=true \wedge false=false$

Answer: false

iii) The exclusive disjunction is $A \oplus B$ . Since$A = true$ and $B = false$ then $A \oplus B=true \oplus false=true$

Answer: true