CBSE BOARD X, asked by tanmayjana250, 1 year ago

Make truth table for followings: (3 Marks) i) p→ (~ q ∨ ~ r) ∧ (p ∨ r) ii) p→(~ r ∧ q) ∧ (p ∧ ~ q)

Answers

Answered by ShruthiS

i) p→ (~ q ∨ ~ r) ∧ (p ∨ r)

ii) p→(~ r ∧ q) ∧ (p ∧ ~ q)

Attachments:

Answered by ashishks1912

i) p→(¬q∨¬r)∧(p∨r)

The truth table for the given problem :

p q r ¬q ¬r (¬q∨¬r) (p∨r) (¬q∨¬r)∧(p∨r) p→(¬q∨¬r)∧(p∨r)

_____________________________________________________

T T T F F F T F F

T T F F T T T T T

T F T T F T T T T

T F F T T T T T T

F T T F F F T F T

F T F F T T F F T

F F T T F T T T T

F F F T T T F F T

ii) p→(¬r∧¬q)∧(p∧¬q)

The truth table for given problem is

p q r ¬q ¬r (¬r∧q) (p∧¬q) (¬r∧q)∧(p∧¬q) p→(¬r∧q)∧(p∧¬q)

_________________________________________________________

T T T F F F F F F

T T F F T T F F F

T F T T F F T F F

T F F T T F T F F

F T T F F F F F T

F T F F T T F F T

F F T T F F F F T

F F F T T F F F T

Explanation:

i) p→(¬q∨¬r)∧(p∨r)

To find the truth table for the given problem :

p q r ¬q ¬r (¬q∨¬r) (p∨r) (¬q∨¬r)∧(p∨r) p→(¬q∨¬r)∧(p∨r)

_____________________________________________________

T T T F F F T F F

T T F F T T T T T

T F T T F T T T T

T F F T T T T T T

F T T F F F T F T

F T F F T T F F T

F F T T F T T T T

F F F T T T F F T

ii) p→(¬r∧¬q)∧(p∧¬q)

The truth table for given problem is

p q r ¬q ¬r (¬r∧¬q) (p∧¬q) (¬r∧¬q)∧(p∧¬q) p→(¬r∧¬q)∧(p∧¬q)

_________________________________________________________

T T T F F F F F F

T T F F T T F F F

T F T T F F T F F

T F F T T F T F F

F T T F F F F F T

F T F F T T F F T

F F T T F F F F T

F F F T T F F F T

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