##### Numercal Answer Type

How many of the disjunctions

- p ∨ ¬q
- ¬p ∨ q
- q ∨ r
- q ∨ ¬r
- ¬q ∨ ¬r

can be made simultaneously true by an assignment of truth values to p, q, and r?

**Answer**

**Things you need to understand**

Lets look at Truth Table of disjunction ( ∨ ):

p |
q |
p ∨ q |

F | F | F |

F | T | T |

T | F | T |

T | T | T |

So, disjunction is **T**rue, when either **p** and **q **or both are **T**rue.

Now,

for p = **T** and q = **T **

(1) , (2) , (3) & (4) is True

and for r = **F**

(5) is True

So,

For p = q = **T **& r = **F **

All five are True

**Ans = 5**

didn' understand the meaning of the question properly , please clear it sir @pritam Sir

sir what about conjunctions ?

then 2 will be ans put, p=t, q=f , r=f

then , 2 will be ans

put p= t, q=f.r=f