Recent questions tagged mathematical-logic

Given the following where $p, q, r, s, t$ are statement variables:(i) $(\sim r \rightarrow \sim r) \vee(\sim q \rightarrow q) \vee(t \rightarrow \sim t)$(ii) $(p \wedge q...

Assume the domain is $\mathbb{R}$. Which of the following statements are true?$\forall x \exists y(x y=1)$$\exists x \forall y\left(x^{2} \geq y^{2}\right)$$\exists x \fo...

Let $S$ be the set of students and $x \in S$. We define the following predicates:$\operatorname{SoC}(x): x$ is a computing student;$\operatorname{CS} 1231(x): x$ has take...

Which of the following statements are true?$\sim(p \rightarrow q) \equiv(p \vee(p \rightarrow \sim q))$$(p \rightarrow(q \vee r)) \leftrightarrow((p \wedge \sim q) \right...

Does there exist a polynomial $q(x)$ with integer coefficients such that $q(1)=2$ and $q(3)=5$ ? Given an example if there is one. Justify, if there is not.

Which of the following statements is/are true for real numbers $x, y$ ?If $x^{2}=y^{2}$ then $x=y$.If $x^{3}=y^{3}$ then $x=y$.If $x < y$ then $x^{2}<y^{2}$If $x < y$ the...

A non-empty collection $\mathcal{S}$ of subsets of a set $U$ is a scattering of $U$ if it satisfies the following condition: for all $A, B \i...

We assume that all the arguments are non-negative integers. The operation x div $2$ divides x by $2$ and returns an integer, discarding the fractional part.int f(int x, i...

((¬p∧q)∧(q→(p→r)))→¬rIs it tautology?

For a polynomial of the form $a_{0}+a_{1} x+\cdots+a_{m} x^{m}$ having degree $m>1$, it is known that the coefficients satisfy the relation $\frac{a_{i-1}}{a_{i-1}+a_{i}}...

What is the meaning of NOT Valid in logic?Does "Not Valid" means Invalid only, Or NOT-Valid can have two possibilities, it can be either INVALID or Satisfiable.As per my ...