propositional logic

Which of the following propositions is tautology?

• $\left(p\vee q\right)\longrightarrow q$

• $p\vee\left(q\longrightarrow p\right)$

• $p\vee\left(p\longrightarrow q\right)$

• none of the above

The proposition 

 $p\wedge\left(\sim p\vee q\right)$  is 

• A tautology

• A contradiction

• Logically equivalent to  $p\wedge q$  

•  All of above

Which of the following is/are tautology?

• $a\vee b\longrightarrow b\wedge c$

• $a\wedge b\longrightarrow\left(b\vee c\right)$

• $a\vee b\longrightarrow\left(b\longrightarrow c\right)$

• none of the above

The truth value of ( 4+3=7) v (5 is not prime)

• True

• False

• neither True nor False

Tags

CCSS.HSS.CP.A.1

Negation of statement (A ∧ B) → (B ∧ C) is _____________

• (A ∧ B) ∧ ¬(B ∧ C)

• ¬(A ∧ B) v ( B v C)

• ¬(A →B) →(¬B ∧ C)

• None of the above

What is the contrapositive of the conditional statement? “The home team misses whenever it is drizzling?”

• If it is drizzling, then home team misses

• If the home team misses, then it is drizzling

• If it is not drizzling, then the home team does not misses

• If the home team wins, then it is not drizzling

Which of the following is not a declarative statement?

• It's right

• He says

• 2 may not be an even integer

• I love you

 $P\longrightarrow\left(Q\longrightarrow R\right)$  is equivalent to

•  $\left(P\wedge Q\right)\longrightarrow R$  

•  $\left(P\vee Q\right)\longrightarrow R$  

•  $\left(P\vee Q\right)\longrightarrow\sim R$  

• None of these

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Which of the following are tautologies?

• $\left(\left(P\vee Q\right)\wedge Q\right)$

  
  

• $\left(\left(P\vee Q\right)\wedge\sim P\right)\longrightarrow Q$

• $\left(\left(P\vee Q\right)\wedge P\right)\longrightarrow P$

• All the above

What are the inverse of the conditional statement “ A positive integer is a composite only if it has divisors other than 1 and itself.”

• “A positive integer is a composite if it has divisors other than 1 and itself.”

• “If a positive integer has no divisors other than 1 and itself, then it is not composite.”

• “If a positive integer is not composite, then it has no divisors other than 1 and itself.”

• None of the mentioned