Verify that validating of the following inference. If one person is more successful than another, then he has worked harder to deserve success. X has not worked harder than Y. Therefore, X is not more successful than Y.

Define proposition with example. Consider the following sentences and determine which of the following is a proposition or not. (i) Dhaka is the capital of Bangladesh. (ii) 2+3=5 (iii) x+2=11 x+y=y+x, for every pair of real numbers x and y.

Suppose that Smartphone A has 256 MB RAM and 32 GB ROM, and the resolution of its camera is 8 MP; Smartphone B has 288 MB RAM and 64 GB ROM, and the resolution of its camera is 4 MP; and Smartphone C has 128 MB RAM and 32 GB ROM, and the resolution of its camera is 5 MP.
Determine the truth value of each of these propositions.

i) Smartphone B has the most RAM of these three smartphones.
ii) Smartphone C has more ROM or a higher resolution camera than Smartphone B.
iii) Smartphone B has more RAM, more ROM, and a higher resolution camera than Smartphone A.
iv) If Smartphone B has more RAM and more ROM than Smartphone C, then it also has a higher resolution camera.

Define logically Equivalences of compound proposition. Show that this implication is a tautology by using truth table. [(p → q) ∩ (q → r)] → (p → r)

What is logic, syntax and semantics ? Write down some propositional logic syntax.

Show that p→(q→r) is logically equivalent to (p∧q)→r