Prove algebraically $\vec{x} = \vec{a} + s\vec{b}, s\in \mathbb R$ and $\vec{x} = \vec{c} + t\vec{d}, t\in \mathbb R$ intersect
119195
Proving two lines in vector form intersect algebraically
59644
Proof of Cartesian product intersection
143979
How can I prove that $|A| + |B| = |A\cup B| + |A\cap B|$?
140440
Proving $(A\times C)\cup(B\times D)\subseteq(A\cup B)\times(C\cup D)$
66283
Let V be a vector space. If every subspace of V is T-invariant, prove that there exist a scalar multiple c such that T=c1v
13421
Let $X,Y,Z$ be subspaces of $V$ so that $X$ is a subspace of $Y$. Prove that $Y\cap (X+Z)=X+(Y\cap Z)$
20736
Prove the relation $R$ in $N \times N$ defined by $(a,b) \simeq (c,d)$ iff $ad=bc$ is an equivalence relation.
95935
Prove A = $(A \cap B) \cup (A \cap B^c)$ using the distributive and associative law.
10107
Prove $A\cup (A\cap B) = A$
81794
Prove that $(ab,cd)=(a,c)(b,d)\left(\frac{a}{(a,c)},\frac{d}{(b,d)}\right)\left(\frac{c}{(a,c)},\frac{b}{(b,d)}\right)$
80876
Proof of $A\cap(B\cup C) = (A\cap B)\cup(A\cap C)$
131132
Proofs using vector properties
79061
show that {$(x_1,x_2,x_3,x_4)\in\mathbb{F}^4$:$x_3=5x_4+b$} is a subspace
88051
$\mathbb R = X^2$ as a Cartesian product
62755
The simplest way of proving that $|\mathcal{P}(\mathbb{N})| = |\mathbb{R}| = c$
83475
Prove Or Disprove: tr(AB)=tr(A)*tr(B)
124786
Prove that V contains a subspace of each dimension